Question

determine if the equation is true or false.
1
$2a^2b^2(a + b) + 4a(a + b) = 8a^3b^2(a + b)$
a. true b. false
2
$xy^2(2x + 3) + 1(2x + 3) = xy^2(2x + 3)$
a. true b. false
3
$105x^5 - 14x^484x^3 = 7x^3(15x^2 - 2x + 12)$
a. true b. false
4
$7x^4 + 63x^3 + x + 9 = (7x^3 + 1)(x + 9)$
a. true b. false

Explanation:

Question 1

Step1: Factor left side

Left side: \(2a^{2}b^{2}(a + b)+4a(a + b)=(a + b)(2a^{2}b^{2}+4a)\)

Step2: Compare with right side

Right side: \(8a^{3}b^{2}(a + b)\)
Since \((a + b)(2a^{2}b^{2}+4a)
eq8a^{3}b^{2}(a + b)\) (unless specific values for \(a,b\) make them equal, generally not), the equation is false.

Step1: Factor left side

Left side: \(xy^{2}(2x + 3)+1(2x + 3)=(2x + 3)(xy^{2}+1)\)

Step2: Compare with right side

Right side: \(xy^{2}(2x + 3)\)
Since \((2x + 3)(xy^{2}+1)
eq xy^{2}(2x + 3)\) (unless \(xy^{2}+1 = xy^{2}\), which is impossible), the equation is false.

Step1: Check left side expression

The left side is \(105x^{5}-14x^{4}84x^{3}\) – there seems to be a typo (missing operator between \(14x^{4}\) and \(84x^{3}\), likely a minus or plus). Assuming it's \(105x^{5}-14x^{4}-84x^{3}\) (common factoring problem structure).

Step2: Factor right side

Right side: \(7x^{3}(15x^{2}-2x + 12)=105x^{5}-14x^{4}+84x^{3}\)
If left side was \(105x^{5}-14x^{4}-84x^{3}\), then it's not equal to right side. Even with the typo, the given left side as \(105x^{5}-14x^{4}84x^{3}\) is invalid, but assuming standard factoring, the equation as written (with typo) is false. So the answer is likely b. False.

Answer:

b. False

Question 2