Question

Factorise :(m+2n)2+101(m+2n)+100

Answer 1

Put m+2n=x
then we get equation is
x^2+101x+100=0
x^2+100x+x+100=0
x(x+100)+1(x+100)=0
(x+100)(x+1)=0
now put the value of x in above equation
(m+2n+100)(m+2n+1)=0

Answer 2

"The value of (m + 2n + 1) (m + 2n + 100) = 0

Given:

$(m + 2n) ^2+101 (m+2n) +100$

To find:

Factorise

Solution:

The given equation is $(m + 2n) ^2+101(m + 2n) +100 ------ (1)$

Let assume m + 2n=k ------ (2)

Substitute the equation (2) in (1)

(k)^2 + 101(k) +100=0

k^2 +101k + 100=0

k^2 + 100k + k +100=0

k (k + 100) + 1 (k + 100)=0

(k+1) (k+100)=0 --- (3)

Substitute the value of k in equation (3)

(m+2n+1)(m+2n+100)=0"