Expand the following: $(4 a - 2 b - 3 c)^{2}$

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Solution

The given expression $(4 a - 2 b - 3 c)^{2}$ can be solved as shown below:

$(4 a - 2 b - 3 c)^{2}$

$= (4 a)^{2} + (- 2 b)^{2} + (- 3 c)^{2} + (2 \times 4 a \times (- 2 b)) + (2 \times (- 2 b) \times (- 3 c)) + (2 \times (- 3 c) \times 4 a)$

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

$= 16 a^{2} + 4 b^{2} + 9 c^{2} - 16 a b + 12 b c - 24 c a$

Hence, $(4 a - 2 b - 3 c)^{2} = 16 a^{2} + 4 b^{2} + 9 c^{2} - 16 a b + 12 b c - 24 c a$ .

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Similar questions

Expand ${(4 a - 2 b - 3 c)}^{2}$

Expand the following, using suitable identities: ${(\frac{1}{4} a - \frac{1}{2} b + 1)}^{2}$ [3 MARKS]

{(a + 2 b + 3 c)}^{2} - {(a - 2 b + 3 c)}^{2} - {6 b}^{2} - 9 b c

{[\frac{1}{4} a - \frac{1}{2} b + 1]}^{2}

{[\frac{1}{4} a - \frac{1}{2} b + 1]}^{2}

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