Which of the following is the correct expansion of 2 a - b 2 - A- a2-b2-a bB- 2 a2-b2-2 a bC- 4 a2-b2-4 a bD- a2-b2-2 a b

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Deducing Formula for (x+y)^2

Which of the ...

Question

Which of the following is the correct expansion of $(2 a + b)^{2}$ ?

a^{2} + b^{2} + a b

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2 a^{2} + b^{2} + 2 a b

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4 a^{2} + b^{2} + 4 a b

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a^{2} + b^{2} + 2 a b

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Solution

The correct option is C $4 a^{2} + b^{2} + 4 a b$
We know, $(x + y)^{2} = x^{2} + 2 x y + y^{2}$
Comparing the given expression with the LHS of this identity, we get,
$x = 2 a$ and $y = b$ .
Then, $(2 a + b)^{2} = (2 a)^{2} + 2 (2 a) (b) + (b)^{2}$
$= 4 a^{2} + 4 a b + b^{2}$
Therefore, the expansion of $(2 a + b)^{2}$ is $4 a^{2} + 4 a b + b^{2}$ .

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Similar questions

Q. The expansion for the identity

{(a - b)}^{2}

is .

Which of the following is correct?
a) $(a - b)^{2} = a^{2} + 2 a b - b^{2}$
b) $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
c) $(a - b)^{2} = a^{2} - b^{2}$
d) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

The expansion of ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ .

If A = [\begin{matrix} a & b b & a \end{matrix}] and A^{2} = [\begin{matrix} α & β β & α \end{matrix}], then

Q. If

A = [\begin{matrix} a & b b & a \end{matrix}]

and

A^{2} = [\begin{matrix} α & β β & α \end{matrix}]

, then

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Which of the following is the correct expansion of (2a+b)2?

The correct option is C 4a2+b2+4abWe know, (x+y)2=x2+2xy+y2 Comparing the given expression with the LHS of this identity, we get, x=2a and y=b. Then, (2a+b)2=(2a)2+2(2a)(b)+(b)2 =4a2+4ab+b2 Therefore, the expansion of (2a+b)2 is 4a2+4ab+b2.

Which of the following is the correct expansion of $(2 a + b)^{2}$ ?