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# If a^{2} + b^{2} = z and ab = y, which of the following is equivalent to 4z + 8y ?

- (a + 2b)
^{2} - (2a +2b)
^{2} - (4a + 4b)
^{2} - (4a + 8b)
^{2}

^{2}^{2}^{2}^{2}## The correct answer is: (2a +2b)^{2}

### Solution:-

- We have given equations

a^{2} + b^{2} = z --------- (1)

ab = y --------- (2)

- We have to find the value of

4z + 8y

- We will put the values of z and y in 4z +8y

4z + 8y = 4(a^{2} + b^{2})+ 8(xy)

= 4a^{2} + 4b^{2}+ 8xy

- We can write 4a
^{2 }as (2a)^{2} as if we squared the term 2a we get 4a^{2}.
- Also, we can write 4b
^{2} as (2b)^{2 }as if we squared the term 2b we get 4b^{2}.
- So, we get

4z + 8y = (2a)^{2 }+ (2b)^{2 }+ 8xy

- On comparing the RHS with the formula u
^{2}+ v^{2} +2uv= (u + v)^{2},

We get, u = 2a , v = 2b , 2uv= 2(2a)(2b)

Therefore, 4z + 8y = (2a + 2b)^{2}

- Therefore the correct answer is option(B) (2a + 2b)
^{2}.

^{2 }as (2a)^{2}as if we squared the term 2a we get 4a^{2}.^{2}as (2b)^{2 }as if we squared the term 2b we get 4b^{2}.^{2}+ v^{2}+2uv= (u + v)^{2},^{2}.### Related Questions to study

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