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

Jun 15, 2016

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

Answer :$7 {x}^{2} - 12 x - 4.$

#### Explanation:

We use the Rule : ${A}^{2} - {B}^{2} = \left(A + B\right) \left(A - B\right) .$

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

Another Method

We know that ${\left(C + D\right)}^{2} = {C}^{2} + 2 C D + {D}^{2.}$

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