Question

Show that (a + b)^2 – (a - b)^2 = 4 ab and using this identity find the value of (75)^2– (25)^2​

Answer 1

Answer:

(75)² - (25)²

(50+25)² - (50-25)²

4 x 50 x 25 = 5000

Hope this help you

Answer 2

Answer:

5000

Step-by-step explanation:

$to \: prove \: ({a + b})^{2} - ({a - b)}^{2} = 4$

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

$= > 2ab + 2ab = 4ab(rhs)$

$now \: we \: have \: to \: solve \: {(75)}^{2} - ( {25})^{2}$

$using \: the \: identity \: {a}^{2} - {b}^{2} = (a + b)(a - b) \: we \: get$

$(75 + 25)(75 - 25) = 100 \times 50 = 5000$