Factorise-2 m 2-20 m -50A- m -5 m -5B- 2 m -5 m -5- 2 m -5 m -5D- 2 m -5 m -5

The correct option is B 2(m + 5)(m + 5)Given, the expression is 2m^2 + 20m + 50. nbsp;=2[m^2 + 10m + 25] ...(i) Now, comparing the expression m^2+10m+25 wit ...

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Byju's Answer

Standard VIII

Mathematics

Factorising Expressions of the Form (x+a)(x+b)

Factorise:2 m...

Question

Factorise:
$2 m^{2} + 20 m + 50.$

(m + 5) (m + 5)

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2 (m + 5) (m + 5)

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2 (m + 5) (m - 5)

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2 (m - 5) (m - 5)

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Solution

The correct option is B $2 (m + 5) (m + 5)$
Given, the expression is
$2 m^{2} + 20 m + 50.$
$= 2 [m^{2} + 10 m + 25] . . . (i)$
Now, comparing the expression $m^{2} + 10 m + 25$ with the identity $x^{2} + (a + b) x + a b$
$We note that,$
$(a + b) = 10 a n d a b = 25$
$S o,$
$(5 + 5) = 10 a n d (5) (5) = 25$
Hence,
$m^{2} + 10 m + 25$
$= m^{2} + 5 m + 5 m + 25$
$= m (m + 5) + 5 (m + 5)$
$= (m + 5) (m + 5)$
Now from (i), we get
$2 m^{2} + 20 m + 50 = 2 (m + 5) (m + 5)$

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