How do you factor $$x^2 - 81$$? This type of expression is known as the difference of squares which is an important method of factorisation found in algebraic equations. In its simplest form, the difference of squares tells us that the difference of two square terms will equal the product of the sum and the difference of their individual square terms. It is written like this: $$ a^2 - b^2 = (a - b)(a + b) $$ ...
Understanding factorisation is crucial in many areas of math, particularly in algebraic expressions and quadratic equations. By factoring, we break down complex expressions into simpler ones, which makes solving problems and simplifying equations much easier. So how do you factorise $1 - x^2$? To factorise $1 - x^2$, apply the difference of two squares method. Applying The Difference Of Squares Method One effective technique for factorising $1 - x^2$ is by using the difference of squares method. This involves recognising that the expression can be written as $(1)^2 - (x)^2$, which follows the general form of $a^2 - b^2$. ...