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

The solution to (a+2b)(3b+a)-(2a-b)^2 is -3a^2+9ab+5b^2

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

simplify

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

- 3 a^{2} + 9 ab + 5 b^{2}

Solution steps

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

Expand

(a + 2 b) (3 b + a) : a^{2} + 5 ab + 6 b^{2}

= a^{2} + 5 ab + 6 b^{2} - (2 a - b)^{2}

Expand

- (2 a - b)^{2} : - 4 a^{2} + 4 ab - b^{2}

= a^{2} + 5 ab + 6 b^{2} - 4 a^{2} + 4 ab - b^{2}

Group like terms

= a^{2} - 4 a^{2} + 5 ab + 4 ab + 6 b^{2} - b^{2}

Add similar elements:

a^{2} - 4 a^{2} = - 3 a^{2}

= - 3 a^{2} + 5 ab + 4 ab + 6 b^{2} - b^{2}

Add similar elements:

5 ab + 4 ab = 9 ab

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

Add similar elements:

6 b^{2} - b^{2} = 5 b^{2}

= - 3 a^{2} + 9 ab + 5 b^{2}

(2 n + 2)!

\frac{- 1}{3} + 1

\frac{k ( k + 1 )}{2} + (k + 1)

2 x^{2} - 11 = 0

\frac{2 x + 4}{3} = \frac{x}{6} - 3

What is (a+2b)(3b+a)-(2a-b)^2 ?
The solution to (a+2b)(3b+a)-(2a-b)^2 is -3a^2+9ab+5b^2