Question

Which one is equivalent?

Answer 1

Step-by-step explanation:

We have to solve the given expression to get the equivalent expression

So,

$(x+4)^2 -(x-4)(x+4)\\= x^2+8x+16-(x^2-16)\\=x^2+8x+16-x^2+16\\= 8x+32$

Now simplifying the options:

Option A:

$4(x+4) = 4x+16$

Option B:

$4(x-4)(x+4)\\=4(x^2-16)\\= 4x^2-64$

Option C:

$(x-4)-(x+4)\\= x-4-x-4\\= -8$

Option D:

$(x+4)[(x+4)-(x-4)]\\= (x+4)[x+4-x+4]\\= (x+4) (8)\\=8x+32$

We can see that option D's simplified form is same as the given expression.

Hence,

Option D: $(x+4)[(x+4)-(x-4)]$ is the correct answer

Keywords: Polynomials, expressions

Learn more about polynomials at:

• brainly.com/question/7932185
• brainly.com/question/788903

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