Question

I. Solve the following using suitable identities :-

(3y + 8z)²
(0.2x - 0.3y)²
(a² + b²)(a² - b²)




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Answer 1

Question

I. Solve the following using suitable identities :-

1. (3y + 8z)²
2. (0.2x - 0.3y)²
3. (a² + b²)(a² - b²)

Answer :-

I.

1) (3y + 8z)²

= {(3y)² + 2×3y×8z + (8z)²}

= 9y² + 48yz + 64z²

2) (0.2x - 0.3y)²

= {(0.2x)² - 2×0.2x×0.3y + (0.3y)²}

= 0.04x² - 0.12xy + 0.09y²

3) (a²+b²)(a²-b²)

= {(a+b)²-2ab}×{(a-b)²+2ab}

= (a²+2ab+b²-2ab) × (a²-2ab+b²+

2ab)

= a²+b² × a²+b²

= a⁴+a⁴b²+b⁴+a²b⁴

= a⁴+b⁴+a⁴b²+a²b⁴

Formula used :-

1. (a+b)² = a²+2ab+b²
2. (a-b)² = a²-2ab+b²
3. a²+b² = (a+b)²- 2ab
4. a²-b² = (a-b)² + 2ab

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