Question

The factored form of 4a3b5 − 16a5b2 + 12a2b3 is ?

Answer 1

4a^2b^2(ab^3-4a^3+3b)

Answer 2

Answer:

The factored form of $4a^3b^5-16a^5b^2+12a^2b^3$ is $4a^2b^2\left(ab^3-4a^3+3b\right)$.

Step-by-step explanation:

To find the factored form of $4a^3b^5-16a^5b^2+12a^2b^3$ you must:

Apply exponent rule: $a^{b+c}=a^ba^c$

$a^2b^3=a^2b^2b,\:a^5b^2=a^2a^3b^2,\:a^3b^5=a^2ab^2b^3$

So, we can write our expression as $4a^2ab^2b^3-16a^2a^3b^2+12a^2b^2b$.

Next, rewrite 12 as $3\cdot \:4$ and -16 as $4\cdot \:4$

$4a^2ab^2b^3+4\cdot \:4a^2a^3b^2+3\cdot \:4a^2b^2b$

Factor out common term: $4a^2b^2$

Therefore,

$4a^3b^5-16a^5b^2+12a^2b^3= 4a^2b^2\left(ab^3-4a^3+3b\right)$