Question

505×502 using identity find

Answer 1

Step-by-step explanation:

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

$505 \times 502 \\ = (500 + 5)(500 + 2) \\ = {500}^{2} + (5 + 2)500 + 5 \times 2 \\ = 250000 + 3500 + 10 \\ = 253510$

Answer 2

$\huge{\mathbb{\red{ANSWER:-}}}$

$\sf{505\times 502}$

$\sf{(500 + 5) (500 + 2)}$

Using Identity :-

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

Solution :-

$\sf{Here \: ,}$

$\sf{x = 500}$

$\sf{a = 5}$

$\sf{b = 2}$

$\sf{So \: ,}$

$\sf{(500)^{2} + (5 + 2)(500) + (5)(2)}$

$\sf{2,50,000 + 7(500) + 10}$

$\sf{2,50,000 + 3500 + 10}$

$\sf{2,53,510}$

Extra Identities :-

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

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

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

4)$\sf{(a + b)^{2} - (a - b)^{2} = 4ab}$