Factorise the following algebraic expression: $$ 14 a^{2} b^{2}+7 a b $$

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UpStudy AI · Accepted Answer

1. Identify the common factor in both terms. The terms $$ 14a^2b^2 $$ and $$ 7ab $$ have a common factor of $$ 7ab $$.

2. Factor out the common factor:
$$
14a^2b^2 + 7ab = 7ab\left(\frac{14a^2b^2}{7ab} + \frac{7ab}{7ab}\right)
$$

3. Simplify the expression inside the parentheses:
$$
\frac{14a^2b^2}{7ab} = 2ab \quad \text{and} \quad \frac{7ab}{7ab} = 1
$$
Thus, the expression becomes:
$$
7ab(2ab + 1)
$$

$$
\boxed{7ab(2ab+1)}
$$
The factored form of the expression is $$ 7ab(2ab + 1) $$.

Factorise the following algebraic expression: \[ 14 a^{2} b^{2}+7 a b \]

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