Question

expand using the formula (2p+q+5)2​

Answer 1

Answer:

(2p + q + 5) ^2

= (2p^2) + (q)^2 + (5)^2 + 2((2p)(q) + (q)(5) + (5)(2p))

= 4p^2 + q^2 + 25 + 4pq + 5q + 20p

Answer 2

Question:

Expand using the formula

$(2p + q + 5) {}^{2}$

Answer :

$(2p + q \: + 5) {}^{2}$

$using \: \: formula \: \: \: (a + b + c) {}^{2} = a{}^{2} + b {}^{2} + c {}^{2} + 2ab + 2bc + 2ac$

So, using this formula

We get ,

$= (2p) {}^{2} \: + q {}^{2} + 5 {}^{2} + 2 \times 2p \times q \: + 2 \times q \times 5 + 2 \times 2p \times 5$

By solving ,

we get :

$4p {}^{2} + q {}^{2} + 25 + 4pq + 10q + 20p$

Hence, expanded.!

Extra :

Identity to be used for solving such questions:

• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac.

Why is this identity to be used ?

Ans : Because for solving this questions the expansion of ( a+b+c)² is necessary.

What is Expansion of (a+b+c)²?

Because ,

expansion of (a+b+c)²

= ( a + b + c ) × ( a + b + c)

= a(a + b + c) + b ( a + b + c) + c ( a + b + c)

= a² +ab + ac + ab + b² + bc + ac + bc + c²

=a² + b² + c² + 2ab + 2bc + 2ac.

Therefore ,

Expansion of (a+b+c)²

which is ,

=a² + b² + c² + 2ab + 2bc + 2ac.