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

1 Answer
Ratnaker Mehta
Jun 15, 2016

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!

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