Question

Factorise: 9a square + 30ab + 25b square

Answer 1

Step-by-step explanation:

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Factor 9a^2+30ab+25b^2

9a2+30ab+25b29a2+30ab+25b2

Rewrite 9a29a2 as (3a)2(3a)2.

(3a)2+30ab+25b2(3a)2+30ab+25b2

Rewrite 25b225b2 as (5b)2(5b)2.

(3a)2+30ab+(5b)2(3a)2+30ab+(5b)2

Check the middle term by multiplying 2ab2ab and compare this result with the middle term in the original expression.

2ab=2⋅(3a)⋅(5b)2ab=2⋅(3a)⋅(5b)

Simplify.

2ab=30ab2ab=30ab

Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2a2+2ab+b2=(a+b)2, where a=3aa=3a and b=5bb=5b.

(3a+5b)2(3a+5b)2