Question

$(a + b ) {}^{2}$
What is the answer​

Answer 1

$\huge \dagger \: \pink{ \huge\frak {Answer}}$

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

• Other Algebraic Identities :-

$\boxed{ \begin{array}{c} \rm(a - b)^{2} = {a}^{2} + {b}^{2} - 2ab \\ \rm (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \rm (a + b) ^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2}b + 3a {b}^{2} \\\rm(a - b) ^{3} = {a}^{3} - {b}^{3} - 3 {a}^{2}b + 3a {b}^{2} \\ (x + \dfrac{1}{x})^{2} = {x}^{2} + \dfrac{1}{ {x}^{2} } + 2 \\ \\ \: (x - \dfrac{1}{x})^{2} = {x}^{2} + \dfrac{1}{ {x}^{2} } - 2 \end{array}}$

$\orange{ \huge \frak{Thankyou}}$

Answer 2

✰ Solution :

• (a + b)² = a² + 2ab + b²

✰If we Prove it :

• (a + b)² = a² + 2ab + b²

✰ The Proof will be :

$\\ \ \mathfrak{ \pmb{L.H.S }}= \tt(a + b)² \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \tt \: \: \: \: \: \: = (a + b)(a + b) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \: = a(a + b ) + b(a + b) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \tt \: = {a}^{2} + ab + ab + {b}^{2} \\ \\ \: \: \: \: \tt \: = {a}^{2} + 2ab + {b}^{2} \\ \\ \tt \: = { \mathfrak{ \pmb{R.H.S}}} \: \: \: \: \: \: \: \: \: \\ \\ \\ \: \: { \underline { \boxed{ \pmb{ \tt{Hence \: Proved}}}}}$

✰ Extra Knowledge :

Some important identities :

• (a – b)² = a² – 2ab + b²

• (a² – b²) = (a + b)(a – b)

• (x + a)(x + b) = x² + (a + b)x + ab

• (a + b)³ = a³ + b³ + 3ab(a + b)

• (a – b)³ = a³ – b³ – 3ab(a – b)

• a³ + b³ = (a + b)(a² – ab + b²)

• a³ – b³ = (a – b)(a² + ab + b²)