Question

pq² +q( p - 1) - 1 factorixe the following

Answer 1

Answer:

Factorisation of $pq^2 + q(p - 1) - 1$ is $(pq - 1)(q + 1)$

Step-by-step explanation:

Step 1: Expand the middle term

$pq^2 + q(p - 1) - 1 = pq^2 + qp - q - 1$

Step 2: Find common factors among them.

Here, we can see $pq^2$ and $pq$ have both $pq$  as a common factor.

And again, we can observe that $-q$ and $-1$ have a common factor which is -1.

So we can write it as the following,

$pq^2 + pq - q - 1 = pq(q + 1) - 1(q + 1)$

Step 3: We can once again identify that $pq(q + 1)$ and $-1(q + 1)$ have $(q + 1)$ as a common factor. So the final result would be: $(pq - 1)(q + 1)$ as the factorised form of the given equation.

$pq^2 + q(p - 1) - 1 = pq ^ 2 + qp - q - 1$

                             $= pq(q + 1) - 1(q + 1)$

                            $= (pq - 1)(q + 1)$