Question

Evaluate using identities.

(756×756) - (244×244)​

Answer 1

Answer:

512000

Step-by-step explanation:

(756×756) - (244×244)​

= 756² - 244²

= (756+244) * (756-244)

= 1000 * 512

= 512000

Answer 2

Algebraic Identities

The following standard algebraic identity will be used to solve the problem:

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

It is called the difference of squares formula.

We have been given that, $(756 \times 756) - (244 \times 244)$. With this information, we have been asked to evaluate the expression using identities.

$\implies (756\times756) - (244\times244)$

Can be re-written as;

$\implies (756^2) - (244^2)$

We know that,

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

By using identities and solving the equation, we get:

$\implies (756 + 244) (756 - 244) \\ \\ \implies 1000 (756 - 244) \\ \\ \implies 1000 \times 512 \\ \\ \implies \boxed{512000}$

Hence, the answer is 512000.