Question

which identity i use to factorise p² – 10 p + 25

Answer 1

You can either split the mid term or use proper identity to factorise any algebraic expression.

Using identity:-

p² - 10 p + 25

= (p)² + (5)² - 2(5)(p) = (p - 5)²

[∵ a² + b² - 2ab = (a - b)²]

= (p - 5)(p - 5)

By splitting the mid term:-

p² - 10 p + 25

= p² - (5 + 5)p + 25

[∵ 5 × 5 = 25; 5 + 5 = 10]

= p² - 5p - 5p + 25

= p(p - 5) - 5(p - 5)

= (p - 5)(p - 5).