Question

Which expression is equivalent to x^4 - 12x^2 + 36?
(1) (x^2 - 6)(^x2 - 6) (3) (6 - x^2)(6 + x^2)
(2) (x^2 + 6)(x^2 + 6) (4) (x^2 + 6)(x^2 - 6)

Answer 1

so the answer is
(x^2 plus or minus 6)(x^2 plus or minus 6)
an easy way to do this is to only look at plus or minus 6
x^4 - 12x^2 + 36   (-12 and 36)

6 x 6 = 36
6 + 6 ≠ -12              (x^2 + 6)(x^2 + 6) is incorrect        

6 x -6 ≠ 36
6 + -6 ≠ -12             (x^2 - 6)(x^2 + 6) is incorrect

-6 x -6 = 36
-6 + -6 = -12         (x^2 - 6)(x^2 - 6) is correct

the answer is (1)

Answer 2

The expression is equivalent to x^4 - 12x^2 + 36 is (x^2 - 6)(x^2 - 6) correct.

We have given that

x^4 - 12x^2 + 36

We have to determine

Which expression is equivalent to x^4 - 12x^2 + 36.

What is the equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

(x^2 plus or minus 6)(x^2 plus or minus 6)

an easy way to do this is to only look at plus or minus 6

x^4 - 12x^2 + 36   (-12 and 36)

6 x 6 = 36

6 + 6 ≠ -12            

(x^2 + 6)(x^2 + 6) is incorrect      

6 x -6 ≠ 36

6 + -6 ≠ -12            

(x^2 - 6)(x^2 + 6) is incorrect

-6 x -6 = 36

-6 + -6 = -12      

Therefore the option (x^2 - 6)(x^2 - 6) is correct

The expression is equivalent to x^4 - 12x^2 + 36 is (x^2 - 6)(x^2 - 6) correct.

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