Question

Factorize the following expression: $10ab+4a+5b+2$

Answer 1

• Factors of $10ab=2\times 5\times a\times b$ …[1]
• Factors of $4a=2\times 2\times a$ …[2]
• Factors of $5b=5\times b$
• From [1] and [2], common factors of $10ab$ and $4a$ is $2a$.

Therefore, $10ab+4a$ can be written as $2a\left(5b+2\right)$ …[3]

• There is no common factor for $5b$and $2$. Hence, consider common factor as $1$. …[4]
• Now, considering [3] and [4], we can write $10ab+4a+5b+2=2a\left(5b+2\right)+1\left(5b+2\right)$

$=\left(2a+1\right)\left(5b+2\right)$

Hence, $\mathbf{10}\mathit{a}\mathit{b}\mathbf{+}\mathbf{4}\mathit{a}\mathbf{+}\mathbf{5}\mathit{b}\mathbf{+}\mathbf{2}$$\mathbf{=}\left(2a+1\right)\left(5b+2\right)$