Question

Which of the following are the factors of the expression $ax-ay+by-bx$ ?

• A. $\left(a-b\right)$ and $\left(x+y\right)$
• B. $\left(a-x\right)$ and $\left(b-y\right)$
• C. $\left(a-b\right)$ and $\left(x-y\right)$
• D. $\left(a-y\right)$ and $\left(b+x\right)$

Answer 1

The correct option is C $\left(a-b\right)$ and $\left(x-y\right)$

Given,
$ax-ay+by-bx$

Grouping the terms, we get
$ax-bx-ay+by$.

Taking $x$ and $y$ common, we get,
$x\left(a-b\right)-y\left(a-b\right)$

$\Rightarrow$ $\left(a-b\right)\left(x-y\right)$

∴ $\left(a-b\right)$ and $\left(x-y\right)$ are the factors of $ax-ay+by-bx$.