Simplify:(i) x2 (x – y) y2 (x + 2y)(ii) (x3 – 2x2 + 5x – 7) (2x

1.	Simplify:(i) x2 (x – y) y2 (x + 2y)(ii) (x3 – 2x2 + 5x – 7) (2x – 3)(iii) (5x + 3) (x – 1) (3x – 2)
Answer» (i) x² (x – y) y² (x + 2y) = x² (x – y) y² (x + 2y) = x²y² (x² + 2xy – xy – 2y²) = x²y² (x² + xy – 2y²) = x⁴y² + x³y³ – 2x²y⁴ (ii) (x³ – 2x² + 5x – 7) (2x – 3) = (x³ – 2x²+ 5x – 7) (2x – 3) = 2x⁴– 4x³ + 10x² – 14x – 3x³ + 6x² – 15x + 21 = 2x⁴ – 7x³ + 16x² – 29x + 21 (iii) (5x + 3) (x – 1) (3x – 2) = (5x + 3) (x – 1) (3x – 2) = (5x² – 2x – 3) (3x – 2) = 15x³ – 6x² – 9x – 10x²+ 4x + 6 = 15x³ – 16x² – 5x + 6

Simplify:(i) x2 (x – y) y2 (x + 2y)(ii) (x3 – 2x2 + 5x – 7) (2x – 3)(iii) (5x + 3) (x – 1) (3x – 2)

Answer»

(i) x² (x – y) y² (x + 2y)

= x² (x – y) y² (x + 2y)

= x²y² (x² + 2xy – xy – 2y²)

= x²y² (x² + xy – 2y²)

= x⁴y² + x³y³ – 2x²y⁴

(ii) (x³ – 2x² + 5x – 7) (2x – 3)

= (x³ – 2x²+ 5x – 7) (2x – 3)

= 2x⁴– 4x³ + 10x² – 14x – 3x³ + 6x² – 15x + 21

= 2x⁴ – 7x³ + 16x² – 29x + 21

(iii) (5x + 3) (x – 1) (3x – 2)

= (5x + 3) (x – 1) (3x – 2)

= (5x² – 2x – 3) (3x – 2)

= 15x³ – 6x² – 9x – 10x²+ 4x + 6

= 15x³ – 16x² – 5x + 6

Simplify:(i) (x – y) (x + y) (x2 + y2) (x4 + y4)(ii) (2x – 1) (2x + 1) (4x2 + 1) (16x4 + 1)
Simplify:(m2 – n2m)2 + 2m3n2
Subtract the sum of 3l – 4m – 7n2 and 2l + 3m – 4n2 from the sum of 9l + 2m – 3n2 and -3l + m + 4n2….
Find the following products:(i) 2a3 (3a + 5b)(ii) -11a (3a + 2b)(iii) -5a (7a – 2b)(iv) -11y2 (3y + 7)
Evaluate each of the following when x = 2, y = -1. (3/5x2y) × (-15/4xy2) × (7/9x2y2)
Find the product of the following binomials:(i) (2x + y) (2x + y)(ii) (a + 2b) (a – 2b)(iii) (a2 + bc) (a2 – bc)
Find the following products: 4/3a (a2 + b2 – 3c2)
Find the product of the binomials: (x3 + 1/x3) (x3 – 1/x3)
If x + 1/x = 9 find the value of x4 + 1/ x4.
Find the product of the binomials:(x4 + 2/x2) (x4 – 2/x2)