Math Snap

STEP 1

Assumptions1. We are given the expression $25a^{} - (a-1)^{}$.
. We are asked to factorise it completely.

STEP 2

The given expression can be rewritten as a difference of two squares. The difference of two squares is a term in algebra where it is the subtraction of the squares of two terms. It can be factorised as $(a+b)(a-b)$.
$$25a^{2} - (a-1)^{2}
$$

STEP 3

We can rewrite $25a^{2}$ as $(5a)^{2}$ and $(a-1)^{2}$ as it is.
$$(5a)^{2} - (a-1)^{2}
$$

STEP 4

Now, we can apply the formula for the difference of two squares, which is $(a+b)(a-b)$.
$$(a + (a-1))(a - (a-1))
$$

implify the expressions within the brackets.
$$(a -1)(4a +1)
$$So, the factorised form of the given expression $25a^{2} - (a-1)^{2}$ is $(a -1)(4a +1)$.