Prove that for any value of x the value of the expression x^4–(x^2–7)(x^2+7) is equal to 49.

Multiplying it out using the distributive property, you have ...

... x^4 -(x^4 -7x^2 +7x^2 -49)

... = x^4 -x^4 +7x^2 -7x^2 +49 . . . . distribute the minus sign

... = x^4(1 -1) +x^2(7 -7) +49 . . . . . . collect like terms

... = 0 +0 + 49 . . . . . . . . . . . . . . . . . .simplify

... = 49

the answer is b.)

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