Question

9 mark for review which expression is equivalent to ((x^2 + 11)^2 - (x - 5)(x + 5))? a (x^4 + 23x^2 - 14) b (x^4 + 23x^2 + 66) c (x^4 + 12x^2 + 121) d (x^4 + x^2 + 146)

Explanation:

Step1: Expand $(x^2 + 11)^2$

Use the formula $(a+b)^2=a^2+2ab+b^2$:
$$(x^2 + 11)^2 = (x^2)^2 + 2(x^2)(11) + 11^2 = x^4 + 22x^2 + 121$$

Step2: Expand $(x-5)(x+5)$

Use the difference of squares $a^2-b^2=(a-b)(a+b)$:
$$(x-5)(x+5) = x^2 - 5^2 = x^2 - 25$$

Step3: Add the two expanded expressions

$$(x^4 + 22x^2 + 121) + (x^2 - 25)$$
Combine like terms:
$$x^4 + (22x^2 + x^2) + (121 - 25) = x^4 + 23x^2 + 96$$

Answer:

B. $x^4 + 23x^2 + 96$