Question

$4a {}^{2} b - 9b ^{3}$
​

Answer 1

$4b {a}^{2} - 9 {b}^{3} \\ b(2a - 3b)(2a + 3b)$

Answer 2

Answer:

$\Large\boxed{b(2a+3b)(2a-3b)}$

Step-by-step explanation:

GIVEN:

$\Large\boxed{\textnormal{SUBJECT: MATH }}}$

4a²b-9b³ (by using with distributive property.)

Isolate by the a or b on one side of the equation.

SOLUTIONS:

First, used exponent rule formula.

$\Large\boxed{\textnormal{EXPONENT RULE}}}$

$\displaystyle A^{B+C}=A^B{A^C}$

$\displaystyle BB^2=B^3$

Rewrite the problem.

$\displaystyle 4a^2b-9bb^2$

Common term of b.

$\displaystyle b(4a^2-9b^2)$

Factor.

Solve. (Simplify/ find the factors/ to find the answer.)

$\displaystyle 4a^2-9b^2$

$\displaystyle (2a)^2-(3b)^2$

Used two squares formula.

$\Large\boxed{\textnormal{TWO SQUARES FORMULA}}}$

$\displaystyle X^2-Y^2=(X+Y)(X-Y)$

$\displaystyle (2a)^2-(3b)^2=(2a+3b)(2a-3b)$

$\Large\boxed{\left(2a+3b\right)\left(2a-3b\right)}$

$\Large\boxed{b(2a+3b)(2a-3b)}$

So, the correct answer is b(2a+3b)(2a-3b).