Question

Factorise: m2- 10 m + 25​

Answer 1

Answer :

m² - 10m + 25 = (m - 5) (m - 5)

Step-by-step explanation :

Given polynomial :  m² - 10m + 25

Let p(x) = m² - 10m + 25

=> It is of the form ax² + bx + c

By comparing, we get

     a = 1, b = -10, c = 325

where

a - coefficient of x²

b - coefficient of x

c - constant term

By sum-product pattern,

>> Find the product of quadratic term [ax²] and constant term [c]

= m² × 25

= 25m²

>> find the factors of "25m²" in pairs

=> (m) (25m)

 => (-m) (-25m)

=> (5m) (5m)

=> (-5m) (-5m)

>> From the above, find the pair that adds to get linear term [bx]

    - 5m - 5m = -10m

>> Split -10m as -5m and -5m

     m² - 10m + 25

    m² - 5m - 5m + 25  

>> Find the common factor,

  m (m - 5) - 5 (m - 5)

   (m - 5) (m - 5)

Therefore, m² - 10m + 25 = (m - 5) (m - 5)