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(a-b)^2 Expansion and Visualisation

Add the follo...

Question

Add the following: a(a+b), b(b+c), c(a+c) and $a^{2}$ + $b^{2}$ + $c^{2}$

+ ab +

+ bc +

+ ac

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+ ab +

+ bc +

+ ac

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+ 2ab +

+ bc +

+ ac

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+ 4ab +

+ 4bc +

+ 4ac

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Solution

The correct option is A + ab + + bc + + ac
$a (a + b) = a^{2} + a b$

$b (b + c) = b^{2} + b c$

$c (a + c) = a c + c^{2}$

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

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Similar questions

Add the following:

$a (a + b), b (b + c), c (a + c) a n d a^{2} + b^{2} + c^{2}$ [2 MARKS]

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

∣ ∣ ∣ ∣ \begin{matrix} b + c & c + a & a + b c + a & a + b & b + c a + b & b + c & c + a \end{matrix} ∣ ∣ ∣ ∣ == 2 (a + b + c) (a b + b c + c a - a^{2} - b^{2} - c^{2})

a, b, c

A, B, C \in R - (0}

a A + b B + c C + \sqrt{(a^{2} + b^{2} + c^{2}) (A^{2} + B^{2} + C^{2})} = 0

\frac{a B}{b A} + \frac{b C}{c B} + \frac{c A}{a C}

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