Question

Factorise: (i) 25m2 –n2
(ii) 42 + 6 –15
(iii) 125a3 – 225 a2b + 135ab2 –27b3

Answer 1

Step-by-step explanation:

1) Factoring:  25m2-n2 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

         A2 - AB + BA - B2 =

         A2 - AB + AB - B2 =

         A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  25  is the square of  5 

Check :  m2  is the square of  m1 

Check :  n2  is the square of  n1 

Factorization is :       (5m + n)  •  (5m - n)

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