Answer:
True.
Step-by-step explanation:
We have been given an equation [tex][x^2 + 8x + 16]\cdot [x^2- 8x+16] = (x^2-16)^2[/tex]. We are asked to determine whether our given equation is true or false.
To answer our given problem, we will simplify left side of our given equation using distributive property as:
[tex]x^2(x^2- 8x+16)+ 8x(x^2- 8x+16)+16(x^2- 8x+16)[/tex]
[tex]x^4- 8x^3+16x^2+ 8x^3-64x^2+128x+16x^2-128x+256[/tex]
Combine like terms:
[tex]x^4- 8x^3+ 8x^3+16x^2+16x^2-64x^2+128x-128x+256[/tex]
[tex]x^4-32x^2+1256[/tex]
Now, we will expand right side of our given equation using perfect square formula as:
[tex](x^2-16)^2=(x^2)^2-2(x)(16)+16^2[/tex]
[tex](x^2-16)^2=x^4-32x+256[/tex]
Since both sides of our given equation are equal, therefore, our given statement is true.
