9(a+b)^2-(a-b)^2
how would you factor that?
9(a^2+2ab+b^2)-(a^2-2ab+b^2)
=8a^2+16ab+8b^2
=8a^2+8ab+8ab+8b^2
=8a(a+b)+8b(a+b)
=8(a+b)(a+b)
=8(a+b)^2
recognize the difference of squares
= ( 3(a+b) + (a-b) (3(a+b) - (a-b) )
= (4a + 2b)(2a + 4b)
= 4(2a+b)(a+2b)
check:
let a = 2 , b = 1
original:
= 9(3)^2 - 1^2
= 80
mine:
= 4(5)(4) = 80
deepali's :
= 8(3^2) = 72 ≠ 80
deepali's answer is not correct.
To factor the expression 9(a+b)^2 - (a-b)^2, we can follow these steps:
Step 1: Expand the expression
Expand (a+b)^2 and (a-b)^2 using the rule (a+b)^2 = a^2 + 2ab + b^2, and (a-b)^2 = a^2 - 2ab + b^2.
9(a+b)^2 - (a-b)^2 = 9(a^2 + 2ab + b^2) - (a^2 - 2ab + b^2)
Step 2: Distribute the coefficients
Distribute the coefficient 9 across the terms in (a^2 + 2ab + b^2):
= 9a^2 + 18ab + 9b^2 - (a^2 - 2ab + b^2)
Step 3: Combine like terms
Combine the terms with the same variables:
= 9a^2 + 18ab + 9b^2 - a^2 + 2ab - b^2
Step 4: Simplify the expression
Simplify the expression by adding or subtracting the coefficients:
= 8a^2 + 20ab + 8b^2
Now, the expression 9(a+b)^2 - (a-b)^2 is factored as 8a^2 + 20ab + 8b^2