Question

$\text{Factorise the expression}15a^{3}b+35a{b}^3.$

• A. $5a(3a^{2}b+7b^3)$
• B. $5ab(3a^2+7b^2)$
• C. $5b(3b^{2}a-7a^3)$
• D. $3b(5b^{2}a-7a^3)$

Answer 1

The correct option is B $5ab(3a^2+7b^2)$

$\text{Given, the expression is}15a^{3}b$ + $35a{b}^3.$

On writing each term as the product of irreducible factors, we get,
$15a^{3}b$ = $3\times 5\times a\times a\times a\times b$
$35a{b}^3$ = $5\times 7\times a\times b\times b\times b$

By taking out the common factors, we get,
$15a^{3}b+35a{b}^3=5ab(3a^2+7b^2)$