Mathematics: 4. Verify the following for a = 3 abd b = 4. a). (a+b)² = a²+2ab+b²b). (a-b)² = a²-2ab+b²c). (a+b)(a-b) = a²-b²Solve this all please..

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4. Verify the following for a = 3 abd b = 4. a). (a+b)²

Ответ:

MichaelM416

10.10.2021

Mathematics

Solution :

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

★ a) (a + b)² = a² + 2ab + b²

Here

↝ a = 3↝ b = 4

Now :-

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

$\longrightarrow\small\sf{(3 + 4)}^{2} = {3}^{2} + 2 \times 3 \times 4 + {4}^{2}$

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

${\longrightarrow{\small{\sf{(7 \times 7)} = 9 + 24 + 16}}}$

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

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

Hence Verified!

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★ b) (a - b)² = a² - 2ab + b²

Here :-

↝ a = 3↝ b = 4

Now :-

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

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

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

${\longrightarrow{\small{\sf{( - 1 \times - 1)} = 9- 24+ 16}}}$

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

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

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

Hence Verified!

━┅━┅━┅━┅━┅━┅━┅━┅━┅━

★ c) (a + b)(a - b) = a² - b²

Here :-

↝ a = 3↝ b = 4

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

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

$\longrightarrow\small\sf{(7)( - 1)= (3 \times 3) - (4 \times 4) }$

$\longrightarrow\small\sf{7 \times - 1= 9 - 16 }$

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

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

Hence Verified!

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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..

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