Question

factorise

1) 25 + 12 x y - 4 x ^2 - 9 y ^2
2).6xy+x^2+9y^2-4a^2
3) x^2-a^2+10ab-25b^2



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Answer 1

Question :-

Factories all of the given .

Answer :-

$(1) \: \: \: \boxed{\red{\sf{(5 - 2x + 3y)(5 + 2x - 3y)} }} \: \\ \\ (2) \: \: \: \boxed{ \green{\sf{ (x + 3y - 2a)(x + 3y + 2a)}}} \\ \\(3) \: \: \: \boxed{\blue{\sf{ (x - a + 5b)(x + a - 5b)}}}$

Explanation :-

$\star \: (1) \sf{25 + 12xy - 4 {x}^{2} - 9 {y}^{2} } \\ \\ \rightarrow \sf{ 25 - \big( {(2 x)}^{2} + {(3y)}^{2} - 12xy \big) } \\ \\ \rightarrow \sf{ {(5)}^{2} - {(2x - 3y)}^{2} }\\ \\ \because \sf{ {x}^{2} - {y}^{2} = (x - y)(x + y) }\\ \\ \rightarrow \boxed{\sf{(5 - 2x + 3y)(5 + 2x - 3y)} }\\ \\ \star \sf{(2) \: 6xy + {x}^{2} + 9 {y}^{2} - 4 {a}^{2} } \\ \\ \rightarrow \sf{ {x}^{2} + {(3y)}^{2} +6xy - {(2a)}^{2} } \\ \\ \rightarrow \sf{ {(x + 3y)}^{2} - {(2a)}^{2} \:} \\ \\ \rightarrow \boxed{ \sf{ (x + 3y - 2a)(x + 3y + 2a)}} \\ \\ \star \: (3) \: \sf{{x}^{2} - {a}^{2} + 10ab - 25 {b}^{2} } \\ \\ \rightarrow \sf{{x}^{2} - {(a - 5b)}^{2} } \\ \\ \rightarrow \boxed{\sf{ (x - a + 5b)(x + a - 5b)}}$

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Answer 2

$\pink{\bold{\underline{\underline{Factorise:-}}}}$

1) 25 + 12 x y - 4 x ^2 - 9 y ^2

2).6xy+x^2+9y^2-4a^2

3) x^2-a^2+10ab-25b^2

$\huge\boxed{\fcolorbox{fuchsia}{grey}{Solution:--}}$

$\textbf{Using these Formulae}$

[1] ( a + b )² = a² + 2ab + b²

[2] ( a – b )² = a² – 2ab + b²

[3] (a² - b²) = (a + b) (a - b)

$\rule{200}{2}$

$\underline{{\colorbox{yellow}{Question(1)}}}$

$25 + 12xy - 4 {x}^{2} - 9 {y}^{2} \\ \\ 25 - (4 {x}^{2} + 9 {y}^{2} - 12xy) \\ \\ (5)^{2} - (2x - 3y)^{2} \\ \\ (5 + 2x - 3y)(5 - 2x + 3y)$

$\rule{200}{2}$

$\underline{{\colorbox{yellow}{Question(2)}}}$

$6xy + {x}^{2} + 9 {y}^{2} - 4 {a}^{2} \\ \\ ( {x}^{2} + (3y)^{2} + 2 \times x \times 3y) - (2a)^{2} \\ \\ (x + 3y)^{2} -(2a)^{2} \\ \\ (x + 3y + 2a)(x + 3y - 2a)$

$\rule{200}{2}$

$\underline{{\colorbox{yellow}{Question(</strong><strong>3</strong><strong>)}}}$

${x}^{2} - {a}^{2} + 10ab \: - 25b^{2} \\ \\ {x}^{2} - (( {a)}^{2} - 2 \times a \times 5b + ( {5b)}^{2} ) \\ \\ {x}^{2} - ( {a - 5b)}^{2} \\ \\ (x - a + 5b)(x + a - 5b)$