Question

Expand (2a-5b-3c)2
please guyss...
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Answer 1

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$\bigstar\mid$Given :-

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

$\bigstar\mid$Algebraic\:Identity :-

$(x + y + {z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2xy + 2yz + 2zx$

$\bigstar\mid$Now,

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

=[(2a) + (-5b) + ${(-3c)]}^{2}$

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

$= 4 {a}^{2} + 25 {b}^{2} + 9 {c}^{2} + 2( - 10ab) + 2(15bc) + 2( - 6ca)$

$= 4 {a}^{2} + 25 {b}^{2} + 9 {c}^{2} - 20ab + 30bc - 12ca$

$\small\mathcal\color{purple}Might\:Help\:You$

Answer 2

Given,

We are given an expression (2a-5b-3c)².

To find,

Expand the expression (2a-5b-3c)².

Solution,

• This expression consists of three variables a, b, and c with coefficients 2, -5 and -3 respectively.

• The expression is of the form (x-y-z)², where x = 2a, y = 5b, z = 3c.

• Expansion of (x-y-z)² is x² + y²+ z²– 2xy + 2yz – 2zx.

• Therefore, the expansion of (2a-5b-3c)²,

(2a)² + (5b)² + (3c)² - 2×(2a)×(5b) + 2×(5b)×(3c) - 2×(3c)×(2a).

• In the further step, we would get.

4a² + 25b² + 9c² - 2×(10ab) + 2×(15bc) -2×(6ca).

• On further simplifying the equation,

4a² + 25b² + 9c² - 20ab + 30bc -12ac.

Hence, the expansion of  (2a-5b-3c)² is 4a² + 25b² + 9c² - 20ab + 30bc -12ac.