Using standard formulae, expand each of the following: (i) (2a2 + 3b)2 (ii) (3x2y + z)2 (iii) (2x+1/3x)²

We know that, ⇒ (a + b)2 = a2 + b2 + 2ab. (i) Given, ⇒ (2a2 + 3b)2 ⇒ (2a2)2 + (3b)2 + 2 × 2a2 × 3b ⇒ 4a4 + 9b2 + 12a2b Hence, (2a2 + 3b)2 = 4a4 + 9b2 + 12a2b . (ii) Given, ⇒ (3x2y + z)2 ⇒ (3x2y)2 + (z)2 + 2 × 3x2y × z ⇒ 9x4y2 + z2 + 6x2yz Hence, (3x2y + z)2 = 9x4y2 + z2 + 6x2yz . (iii) Given, Hence, .

Mathematics

Using standard formulae, expand each of the following:
(i) (2a² + 3b)²
(ii) (3x²y + z)²
(iii) $\Big(2x + \dfrac{1}{3x}\Big)^2$

Expansions

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Answer

We know that,

⇒ (a + b)² = a² + b² + 2ab.

(i) Given,

⇒ (2a² + 3b)²

⇒ (2a²)² + (3b)² + 2 × 2a² × 3b

⇒ 4a⁴ + 9b² + 12a²b

Hence, (2a² + 3b)² = 4a⁴ + 9b² + 12a²b .

(ii) Given,

⇒ (3x²y + z)²

⇒ (3x²y)² + (z)² + 2 × 3x²y × z

⇒ 9x⁴y² + z² + 6x²yz

Hence, (3x²y + z)² = 9x⁴y² + z² + 6x²yz .

(iii) Given,

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

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

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Mathematics

Using standard formulae, expand each of the following:
(i) (2a² + 3b)²
(ii) (3x²y + z)²
(iii) $\Big(2x + \dfrac{1}{3x}\Big)^2$

Expansions

Answer

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