Evaluate each of the following using identities:
(i) (2x - 1/x)²
(ii) (2x+y) (2x-y)
(iii) (a²b - b²a)²
(iv) (a – 0.1) (a +0.1)
(v)(1.5x² - 0.3y²)(1.5x² - 0.3y²)
Answers
(i) (2x - 1/x)²
By using identity: (a – b)² = a² + b² – 2ab :
(2x - 1/x)² = (2x)² + (1/x)² – 2 (2x)(1/x)
= 4x² + 1/x² – 4
(ii) (2x + y) (2x – y)
By using identity : (a – b)(a + b) = a² – b²
(2x + y) (2x – y) = (2x )² – (y)²
= 4x² – y²
(iii) (a²b - b²a)²
By using identity: (a – b)² = a² + b² – 2ab
(a²b - b²a)² = (a²b) ² + (b²a)² – 2(a²b)( b²a)
= a⁴b² + b⁴a²– 2 a³b³
(iv) (a – 0.1) (a + 0.1)
By using identity: (a – b)(a + b) = a²– b²
(a – 0.1) (a + 0.1) = (a)² – (0.1)²
= a² – 0.01
(v) (1.5 x² – 0.3y²) (1.5 x² + 0.3y²)
By using identity: (a – b)(a + b) = a²– b²
(1.5 x² – 0.3y²) (1.5x² + 0.3y²) = (1.5x² ) ²– (0.3y²)²
= 2.25 x⁴ – 0.09y⁴
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Answer:
Step-by-step explanation:
(i) (2x - 1/x)²
By using identity: (a – b)² = a² + b² – 2ab :
(2x - 1/x)² = (2x)² + (1/x)² – 2 (2x)(1/x)
= 4x² + 1/x² – 4
(ii) (2x + y) (2x – y)
By using identity : (a – b)(a + b) = a² – b²
(2x + y) (2x – y) = (2x )² – (y)²
= 4x² – y²
(iii) (a²b - b²a)²
By using identity: (a – b)² = a² + b² – 2ab
(a²b - b²a)² = (a²b) ² + (b²a)² – 2(a²b)( b²a)
= a⁴b² + b⁴a²– 2 a³b³
(iv) (a – 0.1) (a + 0.1)
By using identity: (a – b)(a + b) = a²– b²
(a – 0.1) (a + 0.1) = (a)² – (0.1)²
= a² – 0.01
(v) (1.5 x² – 0.3y²) (1.5 x² + 0.3y²)
By using identity: (a – b)(a + b) = a²– b²
(1.5 x² – 0.3y²) (1.5x² + 0.3y²) = (1.5x² ) ²– (0.3y²)²
= 2.25 x⁴ – 0.09y⁴