If a - b - c - d prove that 5 a - 7 b 2 c - 3 d - 5 c - 7 d 2 a - 3 b

Given #160; a b = c d ad=bc LHS: #160; ( 5a+7b ) ( 2c 3d ) =10ac+14bc 15ad 21bd =10ac+14ad 15ad 21bd =10ac ad 21bd RHS: # ...

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Addition and Subtraction of Algebraic Expression

If a / b = ...

Question

If $\frac{a}{b} = \frac{c}{d}$ prove that
$(5 a + 7 b) (2 c - 3 d) = (5 c + 7 d) (2 a - 3 b)$

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Solution

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a, b, c, d

(5 a + 7 b) (2 c - 3 d) = (5 c + 7 d) (2 a - 3 b)

\vec{a}

\vec{b}

\vec{c}

5 \vec{a} + 6 \vec{b} + 7 \vec{c,} 7 \vec{a} - 8 \vec{b} + 9 \vec{c} and 3 \vec{a} + 20 \vec{b} + 5 \vec{c}

\vec{a} - 2 \vec{b} + 3 \vec{c}, - 3 \vec{b} + 5 \vec{c} and - 2 \vec{a} + 3 \vec{b} - 4 \vec{c}

a, b, c, d

2 a + 3 d : 3 a - 4 d = 2 a^{3} + 3 b^{3} : 3 a^{3} - 4 b^{3}

a + b + c = 0

a^{2} + b^{2} + c^{2} = 1

(3 a + 5 b - 8 c)^{2} + (- 8 a + 3 b + 5 c)^{2} + (5 a - 8 b + 3 c)^{2}

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