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Addition and Subtraction of Algebraic Expression

Solve: a-2b+...

Question

Simplify:
$(a - 2 b + 5 c) (a - b) - (a - b - c) (2 a + 3 c) + (6 a + b) (2 c - 3 a - 5 b)$

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Solution

$\begin{matrix} (a - 2 b + 5 c) (a - b) - (a - b - c) (2 a + 3 c) + (6 a + b) (2 c - 3 a - 5 b) = [a^{2} - a b - 2 a b + 2 b^{2} + 5 a c - 5 b c] - [2 a^{2} + 3 a c - 2 a b - 3 b c - 2 a c - 3 c^{2}] + [12 a c - 18 a^{2} - 30 a b + 2 b c - 3 a b - 5 b^{2}] = a^{2} - a b - 2 a b + 2 b^{2} + 5 a c - 5 b c - 2 a^{2} - 3 a c + 2 a b + 3 b c + 2 a c + 3 c^{2} + 12 a c - 18 a^{2} - 30 a b + 2 b c - 3 a b - 5 b^{2} = a^{2} - 2 a^{2} - 18 a^{2} + 2 b^{2} - 5 b^{2} + 3 c^{2} - a b - 30 a b - 3 a b + 5 a c - 3 a c + 2 a c + 12 a c - 5 b c + 3 b c + 2 b c = - 19 a^{2} - 3 b^{2} + 3 c^{2} - 34 a b + 16 a c A n s . \end{matrix}$

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Similar questions

Q. State true or false

(a - 2 b + 5 c) (a - b) - (a - b - c) (2 a + 3 c) + (6 a + b) (2 c - 3 a - 5 b)

19 c a - 37 a b - 19 a^{2}

(m^{2} - m n + n^{2})

(ii) (a-2b+5c) (a-b)-(a-b-c) (2a+3c)+(6a+b)(2c-3a-5b)

Solve the given expression

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

∣ ∣ ∣ ∣ \begin{matrix} a & a + b & a + b + c 2 a & 3 a + 2 b & 4 a + 3 b + 2 c 3 a & 6 a + 3 b & 10 a + 6 b + 3 c \end{matrix} ∣ ∣ ∣ ∣ = a^{3}

\frac{a}{b} = \frac{c}{d}

\frac{3 a - 5 b}{3 a + 5 b} = \frac{3 c - 5 d}{3 c + 5 d}

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