which expression is equivalent to $7a^{2}b + 10a^{2}b^{2}+14a^{2}b^{3}$?\n$ab(7a^{2}+10ab +…

which expression is equivalent to $7a^{2}b + 10a^{2}b^{2}+14a^{2}b^{3}$?\n$ab(7a^{2}+10ab + 14b^{2})$\n$a^{2}b(7 + 10b+14b^{2})$\n$7a^{2}(b + 3b^{2}+7b^{3})$\n$7a^{2}b^{3}(b^{2}+3b + 7)$

which expression is equivalent to $7a^{2}b + 10a^{2}b^{2}+14a^{2}b^{3}$?\n$ab(7a^{2}+10ab + 14b^{2})$\n$a^{2}b(7 + 10b+14b^{2})$\n$7a^{2}(b + 3b^{2}+7b^{3})$\n$7a^{2}b^{3}(b^{2}+3b + 7)$

Answer

Explanation:

Step1: Factor out the common factor

We look for the greatest - common factor of the terms (7a^{2}b), (10a^{2}b^{2}), and (14a^{2}b^{3}). The common factors among the three terms are (a^{2}b).

Step2: Divide each term by the common factor

(\frac{7a^{2}b}{a^{2}b}=7), (\frac{10a^{2}b^{2}}{a^{2}b} = 10b), (\frac{14a^{2}b^{3}}{a^{2}b}=14b^{2}). So, (7a^{2}b + 10a^{2}b^{2}+14a^{2}b^{3}=a^{2}b(7 + 10b+14b^{2}))

Answer:

(a^{2}b(7 + 10b + 14b^{2})) (corresponding to the second option)