What is (a+b)^2+(a-b)^2 ?

The solution to (a+b)^2+(a-b)^2 is 2a^2+2b^2

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simplify (a+b)^2+(a-b)^2

simplify

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

2 a^{2} + 2 b^{2}

Solution steps

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

Expand

(a + b)^{2} : a^{2} + 2 ab + b^{2}

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

Expand

(a - b)^{2} : a^{2} - 2 ab + b^{2}

= a^{2} + 2 ab + b^{2} + a^{2} - 2 ab + b^{2}

Group like terms

= a^{2} + a^{2} + 2 ab - 2 ab + b^{2} + b^{2}

Add similar elements:

a^{2} + a^{2} = 2 a^{2}

= 2 a^{2} + 2 ab - 2 ab + b^{2} + b^{2}

Add similar elements:

2 ab - 2 ab = 0

= 2 a^{2} + b^{2} + b^{2}

Add similar elements:

b^{2} + b^{2} = 2 b^{2}

= 2 a^{2} + 2 b^{2}

- \frac{2}{4}

\frac{11 !}{11 ! ( 11 - 11 ) !}

m + \frac{2}{3} = \frac{1}{4} m - 1

\frac{1}{2} (1 - 0.95)

\frac{2 x + 5}{5} = \frac{3 x + 1}{2} + \frac{- x + 7}{2}