Question

simplify (2x + 5 )² - (2x - 5 )² ( use identity)​

Answer 1

a² - b² = (a+ b) (a - b)

here

a = 2x + 5

b = 2x - 5

so

(2x + 5 )² - (2x - 5 )²

= (2x + 5 + 2x - 5)(2x + 5 - 2x +5)

= 4x × 10

= 40x

Answer 2

Answer:

I have used the below identity :

$\bullet \: \: \: {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \bullet \: \: \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$

Step-by-step explanation:

${(2x + 5)}^{2} - {(2x - 5)}^{2} \\ = ({(2x)}^{2} + {5}^{2} + (2 \times 2x \times 5)) - ( {(2x)}^{2} + {5}^{2} - (2 \times 2x \times 5)) \\ = ( {4x}^{2} +25 + 20x) - ( {4x}^{2} + 25 - 20x) \\ = \cancel{4 {x}^{2}} \cancel{+ 25} + 20x \cancel{- 4 {x}^{2}}\cancel{ - 25} + 20x \\ \large{ \boxed{= \underline{ \underline{40x}}}}$