Question

how do I Factorise the expression x^2 – 10x + 25

Answer 1

x² - 10x + 25

(x)² -2(x)(5) + (5)²

The above expression form is a² - 2ab + b²

Then we can write (a - b)²

Substitute a  = x and b = 5 in the  expression form is (a - b)²

There fore (x - 5)² or (5 - x)²

Factorise the expression is (x - 5)² or (5 - x)²

Second Method :

x² - 10x + 25

x² - 5x - 5x +25

Take out common term x and -5 in the expression : x² - 5x - 5x +25

x(x - 5) - 5(x - 5)

Take out common term x -5 in the above expression

(x - 5)(x - 5)

Recall : (a - b)² = (a - b)(a - b)

(x - 5)²

Recall :(a - b)² = (b - a)²

or

(5 -x)²

There fore Factorise the expression is (x - 5)² or (5 - x)².