Question

What must be added to 2a2 + 4ab + 2b2 to get 5a2 + 10ab - b2?​

Answer 1

Given:

• 2a² + 4ab + 2b²
• 5a² + 10ab - b²

To find:

• What must be added to 2a² + 4ab + 2b² to get 5a² + 10ab - b²?

Solution:

• The question ∝ (5a² + 10ab - b²) + (- 2a² + 4ab + 2b²)

➯ (5a² + 10ab - b²)⠀⠀⠀⠀⠀⠀ ❬ eq (1) ❭

And,

➯ (- 2a² + 4ab + 2b²)⠀⠀⠀⠀⠀ ❬ eq (2) ❭

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━

« Now, Subtracting eq (2) from eq (1),

➯ 5a² + 10ab - b² - 2a² + 4ab + 2b²

➯ 3a² + 10ab - b² - 4ab + 2b²

➯ 3a² + 6ab - b² - (+2b²)

➯ 3a² + 6ab - 3b²

Hence, 3a² + 6ab -3b² must be added to 2a² + 4ab + 2b² to get 5a² + 10ab - b².

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━

« Now, Verifying this,

➯ 3a² + 6ab - 3b² + 2a² + 4ab + 2b² = 5a² + 10ab - b²

➯ 3a² + 2a² + 6ab + 4ab + 2b² - 3b² = 5a² + 10ab - b²

➯ 5a² + 10ab - b² = 5a² + 10ab - b²

Answer 2

${\sf{\red{\underline{\overline{solution:-}}}}}$

For getting the solution we will Substract equation 1 and 2

5a²+10ab-b²-2a²-4ab-2b²

3a²+10ab+b²-4ab+2b²

3a²+6ab-b²-(+2b²)

= 3a²+6ab-3b²

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