Mathematics

Using standard formulae, expand each of the following:
(i) (5x - 3y)²
(ii) (3a - 7b)²
(iii) $\Big(\dfrac{1}{2}x - \dfrac{3}{2}y\Big)^2$

Expansions

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Answer

We know that,

⇒ (a - b)² = a² + b² - 2ab.

(i) Given,

⇒ (5x - 3y)²

⇒ (5x)² + (3y)² - 2 × 5x × 3y

⇒ 25x² + 9y² - 30xy

Hence, (5x - 3y)² = 25x² + 9y² - 30xy .

(ii) Given,

⇒ (3a - 7b)²

⇒ (3a)² + (7b)² - 2 × 3a × 7b

⇒ 9a² + 49b² - 42ab

Hence, (3a - 7b)² = 9a² + 49b² - 42ab.

(iii) Given,

$\Rightarrow \Big(\dfrac{1}{2}x\ -\ \dfrac{3}{2}y\Big)^2 \\[1em] \Rightarrow \Big(\dfrac{1}{2}x\Big)^2 + \Big(\dfrac{3}{2}y\Big)^2 - 2 \times \dfrac{1}{2}x \times \dfrac{3}{2}y \\[1em] \Rightarrow \dfrac{x^2}{4} + \dfrac{9}{4}y^2 - \dfrac{3}{2}xy$

Hence, $\Big(\dfrac{1}{2}x - \dfrac{3}{2}y\Big)^2 = \dfrac{x^2}{4} + \dfrac{9}{4}y^2 - \dfrac{3}{2}xy$ .

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Mathematics

Using standard formulae, expand each of the following:
(i) (5x - 3y)²
(ii) (3a - 7b)²
(iii) $\Big(\dfrac{1}{2}x - \dfrac{3}{2}y\Big)^2$

Expansions

Answer

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