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

The solution to expand (a-2b+3c)^2 is a^2-4ab+6ac+4b^2-12bc+9c^2

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expand (a-2b+3c)^2

expand

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

a^{2} - 4 ab + 6 a c + 4 b^{2} - 12 b c + 9 c^{2}

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

= (a - 2 b + 3 c) (a - 2 b + 3 c)

Distribute parentheses

= aa + a (- 2 b) + a \cdot 3 c - 2 ba - 2 b (- 2 b) - 2 b \cdot 3 c + 3 c a + 3 c (- 2 b) + 3 c \cdot 3 c

Simplify

aa + a (- 2 b) + a \cdot 3 c - 2 ba - 2 b (- 2 b) - 2 b \cdot 3 c + 3 c a + 3 c (- 2 b) + 3 c \cdot 3 c : a^{2} - 4 ab + 6 a c + 4 b^{2} - 12 b c + 9 c^{2}

= a^{2} - 4 ab + 6 a c + 4 b^{2} - 12 b c + 9 c^{2}

5^{- 1} + 2^{- 1}

\frac{( x + 3 ) ( x - 5 )}{x + 3}

4 - 36 u + 81 u^{2}

(9 + 2 i) (9 - 2 i)

(7 - 8 i)^{- 1}

What is expand (a-2b+3c)^2 ?
The solution to expand (a-2b+3c)^2 is a^2-4ab+6ac+4b^2-12bc+9c^2