Question

using the appropriate identity find the product of the following. (2x²+5)(2x²+5)​

Answer 1

Answer:

= 4x^4 +20x^2+25

Step-by-step explanation:

(a+b)(a+b)=(a+b)^2= a^2+2ab+b^2

=(2x^2+5)(2x^2+5)

=(2x^2+5)^2

= (2x^2)^2 +2(2x^2)(5)+(5)^2

= 4x^4 +20x^2+25

Answer 2

$\sf {(2 {x}^{2} + 5)}(2 {x}^{2} + 5) = 4 {x}^{4} + 20 {x}^{2} + 25$

Given :

The expression (2x² + 5)(2x² + 5)

To find :

The product using the appropriate identity

Identity Used :

$\sf {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

(2x² + 5)(2x² + 5)

Step 2 of 2 :

Find product using the appropriate identity

We use the identity

$\boxed{ \sf {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} }$

Thus the given expression

$\sf = {(2 {x}^{2} + 5)}^{} (2 {x}^{2} + 5)$

$\sf = {(2 {x}^{2} + 5)}^{2}$

$\sf = {(2 {x}^{2} )}^{2} + 2 \times 2 {x}^{2} \times 5 + {5}^{2}$

$\sf = 4 {x}^{4} + 20 {x}^{2} + 25$

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