Question

Factorise 25² + 40 + 16² using suitable identity.​

Answer 1

Here you can see that

25a

2

+40ab+16b

2

=(5a)

2

+2(5a)(4b)+(4b)

2

Comparing this expression with x

2

+2xy+y

2

,

we observe that x=5a and y=4b

Using Identity I, (x+y)

2

≡x

2

+2xy+y

2

, we get

25a

2

+40ab+16b

2

=(5a+4b)

2

=(5a+4b)(5a+4b).

Answer 2

$\rightarrow{{5}^{2}\:+\:40\:+\:{4}^{2}}$

$⟹\:By\:using\:formula\:\:{\rightarrow{{a}^{2}\:+\:2ab\:+\:{b}^{2}\:=\:({a}^{2}\:+\:{b}^{2})}}$

$\rightarrow{{5}^{2}\:+\:2(5)(4)\:+\:{4}^{2}}$

${\color{cyan}{Hence\:{5}^{2}\:+\:2(5)(4)\:+\:{4}{^{2}\:can\:be\:written\:as}}}$

${5}^{2}\:+\:2(5)(4)\:+\:{4}^{2}\:=\:{(5\:+\:4)}^{2}$

$\large{\boxed{\color{lime}{{5}^{2}\:+\:2(5)(4)\:+\:{4}^{2}\:=\:{(5\:+\:4)}^{2}}}}$