Question

simplify using suitable identity: (2x+5)^2-(2x-5)^2​

Answer 1

Hope it helps you...

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Answer 2

$\bf \red{( {2x + 5)}^{2} - ( {2x - 5)}^{2} = 40x}$

Given:

• $( {2x + 5)}^{2} - ( {2x - 5)}^{2}$

To find:

• Simplify using suitable identity.

Solution:

Identity to be used:

$\bf {a}^{2} - {b}^{2} = (a + b)(a - b)$

Step 1:

Compare the polynomial with the identity.

It is clear that;

$a = 2x + 5$

and

$b = 2x - 5$

Step 2:

Apply identity to simplify.

$( {2x + 5)}^{2} - ( {2x - 5)}^{2} = (2x + 5 + 2x - 5)(2x + 5 - 2x + 5)$

or

$( {2x + 5)}^{2} - ( {2x - 5)}^{2} = (4x)(10)$

or

$( {2x + 5)}^{2} - ( {2x - 5)}^{2} = 40x$

Thus,

$\bf ( {2x + 5)}^{2} - ( {2x - 5)}^{2} = 40x$

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