Question

25m^2+40m+16 using identitys,factorise the following :

Answer 1

Answer:

(5m+4)(5m+4)

Step-by-step explanation:

25m^2+40m+16

Mid term break

• Multiply 25 with 16,we get 400 .
• Do factorization of 400 .
• 20 ×20 gives as 400 and 20+20 gives us 40 .
• So we are gonna break the term using 20 and 20

Solution

25m^2+20m+20m+16

take common

5m (5m+4)+4 (5m+4)

(5m+4)(5m+4 )

Answer 2

Given:

Using suitable Identities, Factorise $\rm 25m^2 + 40m + 16$

Solution:

$\therefore \rm 25m^2 + 40m + 16 \\ \rm \implies (5m)^2 + 2 \times (5) \times (4) + (4)^2 \qquad (i)$

So, Using Identity, $(a + b)^2 = a^2 + 2ab + b^2$

On Comparing equation (i) with $\rm (a + b)^2 = a^2 + 2ab + b^2$

We get,

a = 5

b = 4

So,

On Using the $(a+b)^2$ Identity, Factorising,

=> $\sf \bf (5m + 4)^2$

=> $\sf \bf (5m + 4) (5m + 4)$