Question

Factorise -
$100 - 36 {(a + b)}^{2}$

CLUE - Use the Algebraic Identities.

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Answer 1

$\large\mathcal \red \bigstar{\boxed{\purple{ALGEBRAIC\:IDENTITY\:USED}}}$

${a}^{2} - {b}^{2} = (a + b)(a - b)$

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$\large\mathcal\red\bigstar{\underline{\purple{SOLUTION}}}:-$

$100 - 36 {(a + b)}^{2}$

${10}^{2} - {(6(a + b))}^{2}$

$(10 - 6(a + b))(10 + 6(a + b))$

$(10 - 6a - 6b)(10 + 6a + 6b)$

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$\large\mathcal \red\bigstar{\underline{\pink{ANSWER}}}\red\bigstar$

$(10 - 6a - 6b)(10 + 6a + 6b)$

SOME MORE IDENTITIES TO REMEMBER:-

${(a + b)}^2 = {a}^2 + 2ab + {b}^2\\{(a - b)}^2 = {a}^2 - 2ab + {b}^2\\{ a}^2 - {b}^2 = (a + b)(a - b)\\(x + a)(x + b) = {x}^2 + (a + b) x + ab\\{(a + b + c)}^2 = {a}^2 + {b}^2 + {c}^2 + 2ab + 2bc + 2ca\\{(a + b)}^3 = {a}^3 + {b}^3 + 3ab (a + b)\\{(a - b)}3 = {a}^3 - {b}^3 - 3ab (a - b)\\{a}^3 + {b}^3 + {c}^3-3abc = (a + b + c){a}^2 + {b}^2 + {c}^2 - ab - bc - ca$

Answer 2

Factorize :- $100 - 36\:(a + b)^2$

SOLUTION :-

ALGEBRAIC IDENTITY USED :-

$a^2 - b^2 = (a + b)(a - b)$

$100 - 36\:(a + b)^2\\\\\Rightarrow (10)^2 - [6(\:a + b)]^2\\\\\Rightarrow [10 + 6\:(a + b)][10 - 6\:(a + b)]\\\\= \bold {[10 + 6a + 6b][10 - 6a - 6b]}$

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