factorise the following
(1). 5ax - 5bx - a+b
(2). m2 - n2 - mq - nq?
5x (a-b) -1(a-b) = 4(a-b)
now I bet you mean
m^2 - n^2 - m q - nq
(m-n) (m+n) - q (m+n) and continue :)
To factorize the given expressions, let's take each one step by step:
(1) 5ax - 5bx - a + b:
To factorize this expression, we need to look for common factors that we can factor out. In this case, the common factor is 5. So we can rewrite the expression as follows:
5(ax - bx) - (a - b)
Now, let's look at the two terms inside the parentheses individually:
ax - bx:
The terms ax and bx share a common factor of x, so we can factor it out:
x(a - b)
Now, let's plug this back into our original expression:
5(ax - bx) - (a - b) = 5x(a - b) - (a - b)
Now, we can see that we have a common factor of (a - b). Let's factor it out:
(a - b)(5x - 1)
So, the factored form of the expression 5ax - 5bx - a + b is (a - b)(5x - 1).
(2) m^2 - n^2 - mq - nq:
This expression is a quadratic expression in the form of a difference of squares. To factorize it, we need to recognize that it can be written as a difference of squares. Using the formula:
(a^2 - b^2) = (a + b)(a - b)
we can rewrite the expression as follows:
(m^2 - n^2) - (mq + nq)
Now, let's factor out the common factors from each term:
(m + n)(m - n) - q(m + n)
We can see that we have a common factor of (m + n) in both terms. Let's factor it out:
(m + n)(m - n - q)
Therefore, the factored form of the expression m^2 - n^2 - mq - nq is (m + n)(m - n - q).