Using standard formulae, expand each of the following: (i) (4a + 9)2 (ii) (3x + 10y)2 (iii) (√2m + √3n)²

We know that, ⇒ (a + b)2 = a2 + b2 + 2ab. (i) Given, ⇒ (4a + 9)2 ⇒ (4a)2 + (9)2 + 2 × 4a × 9 ⇒ 16a2 + 81 + 72a. Hence, (4a + 9)2 = 16a2 + 81 + 72a. (ii) Given, ⇒ (3x + 10y)2 ⇒ (3x)2 + (10y)2 + 2 × 3x × 10y ⇒ 9x2 + 100y2 + 60xy. Hence, (3x + 10y)2 = 9x2 + 100y2 + 60xy. (iii) Given, Hence, .

Mathematics

Using standard formulae, expand each of the following:
(i) (4a + 9)²
(ii) (3x + 10y)²
(iii) $(\sqrt{2}m + \sqrt{3}n)^2$

Expansions

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Answer

We know that,

⇒ (a + b)² = a² + b² + 2ab.

(i) Given,

⇒ (4a + 9)²

⇒ (4a)² + (9)² + 2 × 4a × 9

⇒ 16a² + 81 + 72a.

Hence, (4a + 9)² = 16a² + 81 + 72a.

(ii) Given,

⇒ (3x + 10y)²

⇒ (3x)² + (10y)² + 2 × 3x × 10y

⇒ 9x² + 100y² + 60xy.

Hence, (3x + 10y)² = 9x² + 100y² + 60xy.

(iii) Given,

$\Rightarrow (\sqrt{2}m + \sqrt{3}n)^2 \\[1em] \Rightarrow (\sqrt{2}m)^2 + (\sqrt{3}n)^2 + 2 \times \sqrt{2}m \times \sqrt{3}n \\[1em] \Rightarrow 2m^2 + 3n^2 + 2\sqrt{6}mn.$

Hence, $(\sqrt{2}m + \sqrt{3}n)^2 = 2m^2 + 3n^2 + 2\sqrt{6}mn$ .

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Mathematics

Using standard formulae, expand each of the following:
(i) (4a + 9)²
(ii) (3x + 10y)²
(iii) $(\sqrt{2}m + \sqrt{3}n)^2$

Expansions

Answer

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