Question

the expression $12a^{2}b^{3}-15ab^{4}$ can be written as $m(4a - 5b)$
what is the value of $m$
a. $3ab^{3}$
b. $3ab^{-1}$
c. $3a^{2}b^{6}$
d. $3a^{3}b^{7}$

Explanation:

Step1: Identify greatest common factor

Find GCF of $12a^2b^3$ and $15ab^4$:

• GCF of coefficients: $\gcd(12,15)=3$
• GCF of $a$-terms: $\gcd(a^2,a)=a$
• GCF of $b$-terms: $\gcd(b^3,b^4)=b^3$

Combined GCF: $3ab^3$

Step2: Factor out GCF from expression

$$12a^2b^3 - 15ab^4 = 3ab^3(4a - 5b)$$

Step3: Match to given form $M(4a-5b)$

Compare factored form to $M(4a-5b)$, so $M=3ab^3$.

Answer:

A. $3ab^3$