What is (3a-b)^2+3(a+b)^2 ?

The solution to (3a-b)^2+3(a+b)^2 is 12a^2+4b^2

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simplify (3a-b)^2+3(a+b)^2

simplify

(3 a - b)^{2} + 3 (a + b)^{2}

12 a^{2} + 4 b^{2}

Solution steps

(3 a - b)^{2} + 3 (a + b)^{2}

Expand

(3 a - b)^{2} : 9 a^{2} - 6 ab + b^{2}

= 9 a^{2} - 6 ab + b^{2} + 3 (a + b)^{2}

Expand

3 (a + b)^{2} : 3 a^{2} + 6 ab + 3 b^{2}

= 9 a^{2} - 6 ab + b^{2} + 3 a^{2} + 6 ab + 3 b^{2}

Group like terms

= 9 a^{2} + 3 a^{2} - 6 ab + 6 ab + b^{2} + 3 b^{2}

Add similar elements:

9 a^{2} + 3 a^{2} = 12 a^{2}

= 12 a^{2} - 6 ab + 6 ab + b^{2} + 3 b^{2}

Add similar elements:

- 6 ab + 6 ab = 0

= 12 a^{2} + b^{2} + 3 b^{2}

Add similar elements:

b^{2} + 3 b^{2} = 4 b^{2}

= 12 a^{2} + 4 b^{2}

x^{2} + 8 = 84

y^{2} - 9 x^{2}

∣ 5 y - 5 ∣ = ∣ 4 y + 6 ∣

\frac{x}{5} + 4 > - 3