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Question

Factorise:
2m2+20m+50.

A
(m+5)(m+5)
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B
2(m+5)(m+5)
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C
2(m+5)(m5)
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D
2(m5)(m5)
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Solution

The correct option is B 2(m+5)(m+5)
Given, the expression is
2m2+20m+50.
=2[m2+10m+25] ...(i)
Now, comparing the expression m2+10m+25 with the identity x2+(a+b)x+ab
We note that,
(a+b)=10 and ab=25
So,
(5+5)=10 and (5)(5)=25
Hence,
m2+10m+25
=m2+5m+5m+25
=m(m+5)+5(m+5)
=(m+5)(m+5)
Now from (i), we get
2m2+20m+50=2(m+5)(m+5)

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