Question

Find the product(2x+y)(2x-y)4x^2+y^2)

Answer 1

GIVEN :

Find the product of the expression $(2x+y)(2x-y)(4x^2+y^2)$

TO FIND :

The product of the given expression.

SOLUTION :

Given expression is  $(2x+y)(2x-y)(4x^2+y^2)$

Solving the given expression as below :

$(2x+y)(2x-y)(4x^2+y^2)$

$=[(2x+y)(2x-y)](4x^2+y^2)$

By using the Algebraic identity :

$(a+b)(a-b)=a^2-b^2$

Here the values are $a=2x$ and b = y

$=[(2x)^2-y^2](4x^2+y^2)$

By using the property of exponents :

$(ab)^m=a^mb^m$

$=[2^2x^2-y^2](4x^2+y^2)$

$=(4x^2-y^2)(4x^2+y^2)$

By using the Algebraic identity :

$(a+b)(a-b)=a^2-b^2$

Here $a=4x^2$ and $b=y^2$

$=[(4x^2)^2-(y^2)^2]$

By using the property of exponents :

$(ab)^m=a^mb^m$

$=4^2(x^2)^2-(y^2)^2$

By using the property of exponents :

$(a^m)^n=a^{mn}$

$=16x^4-y^4$

$(2x+y)(2x-y)(4x^2+y^2)=16x^4-y^4$

∴ the product for the given expression $(2x+y)(2x-y)(4x^2+y^2)$ is $16x^4-y^4$

∴ $(2x+y)(2x-y)(4x^2+y^2)=16x^4-y^4$

Answer 2

Given: (2x+y)(2x-y)4x^2+y^2)

To find: Product of (2x+y)(2x-y)4x^2+y^2)

Solution:

                         (2x+y)(2x-y)4x^2+y^2)   ....................................(eqn 1)

Step 1:

we  will solve the expression in parts.

Firstly we solve (2x + y) (2x - y)

here we can use the formula:

                            (a +b) (a–b) = a² – b ²............(eqn 2)

                here,     a = 2x,  b = y

so put these values of a and b in eqn 2, we get:

                            = (2x)² – (y )²

                            = 4x² – y²

means (2x + y) (2x - y)  = = 4x² – y²

step 2:

put the value of (2x + y) (2x - y)  in eqn 1, we get

                            (4x² – y² ) (4x² + y²)    ..................(eqn 3).

Now solve this eqn 3,  again by using the same formula:

                             (a +b) (a–b) = a² – b²

              Here,    a = 4x² and b = y²

                            = (4x²)² – (y²)²

                           = 16 x⁴ – y⁴

Answer: so the final answer is = 16 x⁴ – y⁴