Plus equals

Role="math" height="22" width="140" alt="12 x plus 8 equals 4 open parentheses... plus... close parentheses">2x2-5x=x...-...{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="23" width="149" alt="2 x squared minus 5 x equals x open parentheses... negative... close parentheses">6x2+8xy+4x=2x...+...+...{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="23" width="235" alt="6 x squared plus 8 x y plus 4 x equals 2 x open parentheses... plus... plus... close parentheses">If the terms involve the same variable(s) to different powers then the highest common factor will include the variable(s) with the smallest power4x5+5x4=x4...+...{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="23" width="163" alt="4 x to the power of 5 plus 5 x to the power of 4 equals x to the power of 4 open parentheses... plus... close parentheses">6x4y7-8x9y5=2x4y5...-...{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="23" width="223" alt="6 x to the power of 4 y to the power of 7 minus 8 x to the power of 9 y to the power of 5 equals 2 x to the power of 4 y to the power of 5 open parentheses... negative... close parentheses">The highest common factor could also contain bracketsx+12+5x+1=x+1...+...{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="23" width="254" alt="open parentheses x plus 1 close parentheses squared plus 5 open parentheses x plus 1 close parentheses equals open parentheses x plus 1 close parentheses open parentheses... plus... close parentheses">x+1x+2x+3+x+1x+2x+4=x+1x+2...+...{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="22" width="478" alt="open parentheses x plus 1 close parentheses open parentheses x plus 2 close parentheses open parentheses x plus 3 close parentheses plus open parentheses x plus 1 close parentheses open parentheses x plus 2 close parentheses open parentheses x plus 4 close parentheses equals open parentheses x plus 1 close parentheses open parentheses x plus 2 close parentheses open parentheses... plus... close parentheses">Then find what you need to multiply the highest common factor by to get each termYou might need to use the index law: xa×xb=xa+b{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="23" width="107" alt="x to the power of a cross times x to the power of b equals x to the power of a plus b end exponent">Worked Example(a) Expand and simplify x+4x4-5x3+4x2-7x{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="23" width="200" alt="open parentheses x plus 4 close parentheses open parentheses x to the power of 4 minus 5 x cubed plus 4 x squared minus 7 x close parentheses">.The second bracket has more than two terms so turn the expression into single bracket expansionsx+4x4-5x3+4x2-7x=xx4-5x3+4x2-7x+4x4-5x3+4x2-7x=x5-5x4+4x3-7x+4x4-20x3+16x2-28x{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="50" width="555" alt="table row cell open parentheses x plus 4 close parentheses open parentheses x to the power of 4

Basic Expanding & FactorisingHow do I expand brackets?Expanding brackets means multiplying all the terms inside a bracket by the term outside of the bracketFor GCSE Mathematics you will have learnt how to expand a single bracketMultiply each term inside the bracket by the term outside the bracket2x3x-4y+5=2x×3x-2x×4y+2x×5=6x2-8xy+10x{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="49" width="319" alt="table row cell 2 x open parentheses 3 x minus 4 y plus 5 close parentheses end cell equals cell 2 x cross times 3 x minus 2 x cross times 4 y plus 2 x cross times 5 end cell row blank equals cell 6 x squared minus 8 x y plus 10 x end cell end table">You will also have learnt how to expand double bracketsYou can turn this into two single brackets by multiplying each term inside one bracket by the other bracketFor Level 2 Further Mathematics you might get more than two terms in a bracketTherefore using a grid or turning the expression into single brackets will be more helpful than using FOIL2x+53x-4y+5=2x3x-4y+5+53x-4y+5=6x2-8yx+10x+15x-20y+25=6x2+-8xy+25x-20y+25{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="76" width="409" alt="table row cell open parentheses 2 x plus 5 close parentheses open parentheses 3 x minus 4 y plus 5 close parentheses end cell equals cell 2 x open parentheses 3 x minus 4 y plus 5 close parentheses plus 5 open parentheses 3 x minus 4 y plus 5 close parentheses end cell row blank equals cell 6 x squared minus 8 y x plus 10 x plus 15 x minus 20 y plus 25 end cell row blank equals cell 6 x squared plus negative 8 x y plus 25 x minus 20 y plus 25 end cell end table">A bracket that is raised to the power of 2 can also be written as a double bracketx+y+z2=x+y+zx+y+z{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="23" width="250" alt="open parentheses x plus y plus z close parentheses squared equals open parentheses x plus y plus z close parentheses open parentheses x plus y plus z close parentheses">Write as a double bracket and then expandDo not just square each term inside the bracketBe very careful when working with negativesRemember to simplify expressions where possibleHow do I factorise out a term from an expression?Factorising is the opposite of expandingFirstly find the highest common factor of each term in the expression and put this outside a bracketThe highest common factor could be a single number or a variable or both 12x+8=4...+...{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}"

Last character Divide (/) for division Multiply (*) for multiplication Minus (-) for subtraction Plus (+) for addition Plus/Minus (+/-) (F3) Decimal point (.) Square (x²) Fraction (⅟x) Parentheses for controlling calculation order How to calculate percentages The Percent (F1) key is invaluable for calculating discounts and taxes on items. For instance, if you're shopping and want to determine the tax on a $20 item with a 12% tax rate, enter "12%20" to find that the tax amounts to $2.40. To calculate the total cost, simply use the addition key: "20+12%" yields $22.40. For discounts, like a 20% store-wide reduction, key in "20-20%" to find the reduced price, then add the tax if applicable. For example, "20-20%+12%" results in a final cost of $17.92. How to Calculate the Square of a Number The Square (x²) key multiplies a number by itself. For instance, entering "9²" equals 81, as 9 multiplied by 9 equals 81. How to Calculate the Square Root of a Number The Square Root (F2) key calculates the square root of a number, which, when multiplied by itself, yields the original number. For example, "9√" equals 3, or "3+9√" equals 9. How the Fraction Key Works The Fraction (⅟x) key, also known as the reciprocal key, generates a fraction with "1 over x." For instance, entering "⅟4" results in 0.25, as 1 divided by 4 equals 0.25. How to Use the Plus/Minus (+/-) Key The Plus Minus (+/-) key converts a value from positive to negative or vice

Equals cell open parentheses x plus 1 close parentheses open parentheses 2 x plus 3 plus x minus 2 close parentheses end cell row blank equals cell open parentheses x plus 1 close parentheses open parentheses 3 x plus 1 close parentheses end cell end table" data-type="working">The whole expression is now fully simplified (but it's always worth checking!)(x+1)(3x+1){"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="22" width="117" alt="" data-type="finalAnswer">Expanding Triple BracketsHow do I expand three brackets?Multiply out any two brackets using a standard method and simplify this answer (collect any like terms)Replace the two brackets above with one long bracket containing the expanded resultExpand this long bracket with the third (unused) bracketThis step often looks like (x + a)(x2 + bx + c)Every term in the first bracket must be multiplied with every term in the second bracketThis leads to six terms A grid can often help to keep track of all six terms, for example (x + 2)(x2 + 3x + 1)add all the terms inside the grid (diagonals show like terms) to get x3 + 2x2 + 3x2 + 6x + x + 2collect like terms to get the final answer of x3 + 5x2 + 7x + 2Simplify the final answer by collecting like terms (if there are any)It helps to put negative terms in brackets when multiplyingWorked ExampleExpand 2x-3x+43x-1{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="22" width="163" alt="open parentheses 2 x minus 3 close parentheses open parentheses x plus 4 close parentheses open parentheses 3 x minus 1 close parentheses">.Start by expanding the first two sets of brackets and simplify by collecting 'like' terms2x-3x+4=2x×x+2x×4+-3×x+-3×4=2x2+8x-3x-12=2x2+5x-12{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="102" width="281" alt="table row blank blank cell open parentheses 2 x minus 3 close parentheses open parentheses x plus 4 close parentheses end cell row blank equals cell 2 x cross times x plus 2 x cross times 4 plus open parentheses negative 3 close parentheses cross times x plus open parentheses negative 3 close parentheses cross times 4 end cell row blank equals cell 2 x squared plus 8 x minus 3 x minus 12 end cell row blank equals cell 2 x squared plus 5 x minus 12 end cell end table" data-type="working">Rewrite the original expression with the first two brackets expanded2x2+5x-123x-1{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" role="math" height="23" width="167" alt="open parentheses 2 x squared plus 5 x minus 12 close parentheses open parentheses 3 x minus 1 close parentheses" data-type="working">Multiply all of the terms in the