Evaluate (4x+y)2by suitable identitya)4x2+y2+8x b)4x+y+8xyc)16x2+y2+8xyd)16x2+y2+8Correct answer is option 'C'. Can you explain this answer?

Question

Evaluate (4x+y)2by suitable identitya)4x2+y2+8x      b)4x+y+8xyc)16x2+y2+8xyd)16x2+y2+8Correct answer is option 'C'. Can you explain this answer?

Answer

{this expression looks like (a+b)^2 }
(a+b)^2= a^2 +2ab+b^2
(4x+y)^2 =(4x)^2 +2(4x)(y)+(y)^2
=16x^2 +8xy+ y^2

Answer

Answer

Given that (4x+y)^2
using identity (a+b)^2=a^2+2ab+b^2
here a=4x and b=y
therefore (4x+y)^2=(4x)^2+2(4x)(y)+(y)^2
=16x^2+8xy+y^2
=16x^2+y^2+8xy
hence option (c) is correct

Answer

The given expression is (4xy)^2. To evaluate this expression, we need to use the suitable identity, which is the square of a binomial.

The square of a binomial can be expressed as (a + b)^2 = a^2 + 2ab + b^2, where a and b are any real numbers.

In our given expression, a = 4x and b = y. Plugging these values into the identity, we get:

(4xy)^2 = (4x)^2 + 2(4x)(y) + (y)^2

Simplifying further:

= 16x^2 + 8xy + y^2

Now let's compare the simplified expression with the given answer options:

a) 4x^2y^2 + 8x
b) 4xy + 8xy
c) 16x^2y^2 + 8xy
d) 16x^2y^2 + 8

We can see that option C, 16x^2y^2 + 8xy, matches the simplified expression.

Hence, the correct answer is option C, 16x^2y^2 + 8xy.

Answer

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