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### Grade 7 - Mathematics4.49 Special Products and Expansions - Formulas

Formulas:
(a+b)2 = (a+b)(a+b) =a2+2ab+b2
(a-b)2 = (a-b)(a-b) =a2-2ab+b2
(a+b)3 = (a+b)(a+b)(a+b) = (a+b)(a2+2ab+b2) =a3+3ab2+3a2b+b3
(a-b)3 = (a-b)(a-b)(a-b) = (a-b)(a2-2ab+b2) =a3+3ab2-3a2b+b3
 Sum of squares: a2+b2 =(a+b)2- 2ab a2+b2 =(a-b)2+ 2ab Difference of squares: a2-b2 = (a+b)(a-b) Sum of cubes: a3 + b3 = (a2 - ab + b2)(a + b) Difference of cubes: a3 - b3 = (a2 + ab + b2)(a - b)

Directions:Solve the following problems. Also write two examples for each formula above.
 Q 1: Multiply (7x+7y) with (6x+3).42x2+15x+42xy+21y42x2+21x+46xy+21y42x2+21x+42xy+21y Q 2: Multiply (6x2+7x-1) with x2.6x4-7x3-x26x4+7x3+x26x4+7x3-x2 Q 3: Multiply (7x2-6x+7) with 6x.42x3+36x2+42x42x3-36x2+42x42x3-36x2-42x Q 4: If x=2, then find the value of 8x2+6x+7.475149 Q 5: Multiply (x-7) with (x2+1).x3-7x2+x+7x3-7x2+x-7x3-7x2-x+7 Q 6: Multiply (6x+7) with (7x+3).42x2+65x+2142x2+67x+2142x2+67x+24 Q 7: Multiply (3x-2y) with (3x+y).9x2-3xy+2y29x2-3xy+3y29x2+3xy+2y29x2-3xy-2y2 Q 8: Multiply (6x+7) with (2y+3).12xy+18x+14y+2012xy+18x+14y+2112xy+18y+14x+21 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!