Question

4. Verify the following for a = 3 abd b = 4.

a). (a+b)² = a²+2ab+b²
b). (a-b)² = a²-2ab+b²
c). (a+b)(a-b) = a²-b²

Solve this all please..​

Answer 1

Solution :

Verify the following for a = 3 and b = 4.

★ a) (a + b)² = a² + 2ab + b²

Here

• ↝ a = 3
• ↝ b = 4

Now :-

`\longrightarrow\small\sf{(a + b)}^(2) = {a}^(2) + 2ab + {b}^(2)`

`\longrightarrow\small\sf{(3 + 4)}^(2) = {3}^(2) + 2 * 3 * 4 + {4}^(2)`

`{\longrightarrow{\small{\sf{(7)}^(2) = {(3 * 3)} + 6 * 4 + {(4 * 4)}}}}`

`{\longrightarrow{\small{\sf{(7 * 7)} = 9 + 24 + 16}}}`

`{\longrightarrow{\small{\sf{49 = 49}}}}`

`\longrightarrow{\small{\sf{\underline{\underline{LHS = RHS}}}}}`

Hence Verified!

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★ b) (a - b)² = a² - 2ab + b²

Here :-

• ↝ a = 3
• ↝ b = 4

Now :-

`\longrightarrow\small\sf{(a - b)}^(2) = {a}^(2) - 2ab + {b}^(2)`

`\longrightarrow\small\sf{(3 - 4)}^(2) = {3}^(2) - 2 * 3 * 4 + {4}^(2)`

`\longrightarrow\small\sf{( - 1)}^(2) = {(3 * 3)} - 6* 4 + {(4 * 4)}`

`{\longrightarrow{\small{\sf{( - 1 * - 1)} = 9- 24+ 16}}}`

`{\longrightarrow{\small{\sf{1} = 25- 24}}}`

`{\longrightarrow{\small{\sf{1 = 1}}}}`

`\longrightarrow{\small{\sf{\underline{\underline{LHS = RHS}}}}}`

Hence Verified!

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★ c) (a + b)(a - b) = a² - b²

Here :-

• ↝ a = 3
• ↝ b = 4

`\longrightarrow\small\sf{(a + b)(a - b)= {a}^(2) - {b}^(2) }`

`\longrightarrow\small\sf{(3 + 4)(3- 4)= {3}^(2) - {4}^(2) }`

`\longrightarrow\small\sf{(7)( - 1)= (3 * 3) - (4 * 4) }`

`\longrightarrow\small\sf{7 * - 1= 9 - 16 }`

`\longrightarrow\small\sf{-7= - 7}`

`\longrightarrow{\small{\sf{\underline{\underline{LHS = RHS}}}}}`

Hence Verified!