Question

$9 \times 8^2 - 9 \times 2 ^{2}$

Answer 1

Hi there!

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Given :

9 × 8² - 9 × 2²

This question can be solved using two methods ;

Method I :

9 × 8² - 9 × 2²

It can be written as ;

3² × 8² - 3² × 2²

We will use

aⁿ × bⁿ = ( ab )ⁿ

So,

( 3 × 8 )² - ( 3 × 2 )²

⇒ (24)² - (6)²

Using identity :

a² - b² = ( a + b ) ( a - b )

⇒ (24 + 6) (24 - 6)

⇒ 30 × 18

⇒ 540

Method II :

9 × 8² - 9 × 2²

⇒ 9 × 64 - 9 × 4

⇒ 576 - 36

⇒ 540

Hence,  The final answer is 540.

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Thanks for the question !

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Answer 2

$\underline{\bold{Solution:-}}$

$9\times {8}^{2} - 9 \times {2}^{2} \\ \\ \bold{Taking \: common \: 9 \:} \\ \\ = 9 \times ( {8}^{2} - {2}^{2} ) \\ \\ = 9 \times (8 \times 8 - 2 \times 2) \\ \\ \bold{Taking \: common \: 4 \:} \\ \\ = 9 \times 4 \times (8 \times 2 - 1) \\ \\ = 36 \times (16 - 1) \\ \\ = 36 \times 15 \\ \\ = 540$

The answer of the question is 540.