Step-by-step explanation:
We have to solve the given expression to get the equivalent expression
So,
[tex](x+4)^2 -(x-4)(x+4)\\= x^2+8x+16-(x^2-16)\\=x^2+8x+16-x^2+16\\= 8x+32\\[/tex]
Now simplifying the options:
Option A:
[tex]4(x+4) = 4x+16[/tex]
Option B:
[tex]4(x-4)(x+4)\\=4(x^2-16)\\= 4x^2-64[/tex]
Option C:
[tex](x-4)-(x+4)\\= x-4-x-4\\= -8[/tex]
Option D:
[tex](x+4)[(x+4)-(x-4)]\\= (x+4)[x+4-x+4]\\= (x+4) (8)\\=8x+32[/tex]
We can see that option D's simplified form is same as the given expression.
Hence,
Option D: [tex](x+4)[(x+4)-(x-4)][/tex] is the correct answer
Keywords: Polynomials, expressions
Learn more about polynomials at:
- brainly.com/question/7932185
- brainly.com/question/788903
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