Question

Show that,
(a + b) ² = a² + 2ab + b²​

Answer 1

GIVEN :-

$\implies \bf \: (a \: + b) ^{2} = a ^{2} + 2ab + b ^{2}$

TO PROVE :-

$\implies \bf \: (a \: + b) ^{2} = a ^{2} + 2ab + b ^{2}$

SOLUTION :-

Take L.H.S ,

$\implies \sf \: (a + b) ^{2}$

It can be written as,

$\implies \sf \: (a \: + b)(a + b) \\ \\ \implies \sf \: a(a + b) + b(a + b) \\ \\ \implies \sf \: a ^{2} + ab \: + ab + b^{2} \\ \\ \implies \sf \: \: a ^{2} + 2ab + b ^{2}$

L.H.S = R.H.S

HENCE VERIFIED

ADDITIONAL INFORMATION :-

➣ ( x + y )² = x² + 2xy + y²

➣ ( x - y )² = x² - 2xy + y²

➣ ( a + b ) ( a + b ) = ( a + b )²

➣ ( a - b ) ( a - b ) = ( a - b )²

➣ ( a + b ) ( a - b ) = a² - b²

➣ ( x + a ) ( x + b ) = x² + x ( a + b ) + ab

Answer 2

$\red{ \underline \bold{given :(a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} }} \\ \\ \orange{ \underline \bold{:: : : :solution }} \: \\ \\ \orange{ \underline \bold{:take \: l . h .s}} \: \\ \\ \orange{ \underline \bold{:it \: can \: be \: written}} \: \\ \\ \tt : \implies \orange{ \underline \bold{: (a + b(a + b)}} \: \\ \\ \tt : \implies \: \orange{ \underline \bold{: a(a + b) + b(a + b)}} \: \\ \\ \tt : \implies\orange{ \underline \bold{: {a}^{2} + ab + ab + {b}^{2} }} \: \\ \\ \tt : \implies\orange{ \underline \bold{: {a}^{2} + 2ab + {b}^{2} }} \\ \\ itz \: shiwam............................... \:$




ADDITIONAL INFORMATION :-

➣ ( x + y )² = x² + 2xy + y²

➣ ( x - y )² = x² - 2xy + y²

➣ ( a + b ) ( a + b ) = ( a + b )²

➣ ( a - b ) ( a - b ) = ( a - b )²

➣ ( a + b ) ( a - b ) = a² - b²

➣ ( x + a ) ( x + b ) = x² + x ( a + b ) + ab