Question

How do you solve `16x^2 - (3x + 2)^2`?

Answer 1

I feel that the question should be "How do you simplify `16x^2-(3x+2)^2?`"

Answer :`7x^2-12x-4.`

Explanation:

We use the Rule : `A^2-B^2=(A+B)(A-B).`

Given Expression (Exp.) = `16x^2-(3x+2)^2 = (4x)^2-(3x+2)^2`. Now, applying the above Rule, we get
Expression `={4x+(3x+2)}{4x-(3x+2)} = (7x+2)(4x-3x-2)=(7x+2)(x-2)=7x(x-2)+2(x-2)=7x^2-14x+2x-4=7x^2-12x-4.`

Another Method

We know that `(C+D)^2=C^2+2CD+D^2.`

Using this formula to expand the last term of the given expression, we get, the given Exp. `= 16x^2-(3x+2)^2=16x^2-{(3x)^2 +2*3x*2+(2)^2}=16x^2-(9x^2+12x+4)=16x^2-9x^2-12x-4=7x^2-12x-4,` as before!