Question

Factorise the following expression



49a² – 25b² + 80bc – 64c²


please answer ​

Answer 1

${\boxed{\underline{\tt{\orange{Required \: Answer:-}}}}}$

★GIVEN:-

$\displaystyle \sf{49a² – 25b² + 80bc – 64c² }$

★FORMULA USED:-

• $\displaystyle \sf{\: x^2 - y^2 = (x+y)(x-y)}$

• $: \longrightarrow\displaystyle \sf{\: x^2 + y^2 -2xy = (x-y)^2 }$

★SOLUTION:-

$: \longrightarrow\displaystyle \sf{ {(7a)}^{2} - {( 5b)}^{2} + 2 \times (5b)( 8c) - {(8c)}^{2} }$

$: \longrightarrow\displaystyle \sf{( - {(5b)}^{2} + 2(5b)(8c) - {(8c)}^{2} ) + {(7a)}^{2} }$

take - common:-

$: \longrightarrow\displaystyle \sf{ - (( {5b)}^{2} - 2(5b)(8c) + {8c)}^{2}) + {(7a)}^{2} } \\ \\ : \longrightarrow\displaystyle \sf{ - ( {5b - 8c)}^{2} + {(7a)}^{2} } \\ \\ : \longrightarrow\displaystyle \sf{{(7a)}^{2} - {(57ab - 8c)}^{2} } \\ \\ : \longrightarrow\displaystyle \sf{7a + (5b - 8c) \: and \: 7a - (5b - 8c)} \\ \\ : \longrightarrow\displaystyle \sf{ \pink{7a + 5b - 8c \: \: {and} \: \: 7a - 5b + 8c}}$

Answer 2

${\pmb{\underline{\sf{Required \: Solution....}}}}$

$: \implies49a {}^{2} - (25b {}^{2} - 80bc + 64c {}^{2} \\ : \implies49a {}^{2} - (5b - 8c) {}^{2} \\ : \implies(7a - (5b - 8c)) \times (7a + (5b - 8c)) \\ \boxed {: \implies(7a - 5b + 8c) \times (7a + 5b - 8c)}$

Answer : ( 7a - 5b + 8c ) × (7a+ 5b - 8c)

Formula Used :

• a² - 2ab + b² = ( a- b) ²
• a² - b² = ( a- b) ( a+ b)

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$\:\sf\blue{hope \: this \: helps \: you!! \: }$

@Mahor2111

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