Simplify:(i) (5 – x) (6 – 5x) (2 – x)(ii) (2x2 + 3x – 5) (3x2

1.	Simplify:(i) (5 – x) (6 – 5x) (2 – x)(ii) (2x2 + 3x – 5) (3x2 – 5x + 4)(iii) (3x – 2) (2x – 3) + (5x – 3) (x + 1)
Answer» (i) (5 – x) (6 – 5x) (2 – x) = (5 – x) (6 – 5x) (2 – x) = (x² – 7x + 10) (6 – 5x) = -5x³+ 35x² – 50x + 6x² – 42x + 60 = 60 – 92x + 41x² – 5x³ (ii) (2x² + 3x – 5) (3x² – 5x + 4) = (2x² + 3x – 5) (3x² – 5x + 4) = 6x⁴ + 9x³ – 15x² – 10x³ – 15x²+ 25x + 8x² + 12x – 20 = 6x⁴ – x³ – 22x²+ 37x – 20 (iii) (3x – 2) (2x – 3) + (5x – 3) (x + 1) = (3x – 2) (2x – 3) + (5x – 3) (x + 1) = 6x² – 9x – 4x + 6 + 5x² + 5x – 3x – 3 = 11x² – 11x + 3

Simplify:(i) (5 – x) (6 – 5x) (2 – x)(ii) (2x2 + 3x – 5) (3x2 – 5x + 4)(iii) (3x – 2) (2x – 3) + (5x – 3) (x + 1)

Answer»

(i) (5 – x) (6 – 5x) (2 – x)

= (5 – x) (6 – 5x) (2 – x)

= (x² – 7x + 10) (6 – 5x)

= -5x³+ 35x² – 50x + 6x² – 42x + 60

= 60 – 92x + 41x² – 5x³

(ii) (2x² + 3x – 5) (3x² – 5x + 4)

= (2x² + 3x – 5) (3x² – 5x + 4)

= 6x⁴ + 9x³ – 15x² – 10x³ – 15x²+ 25x + 8x² + 12x – 20

= 6x⁴ – x³ – 22x²+ 37x – 20

(iii) (3x – 2) (2x – 3) + (5x – 3) (x + 1)

= (3x – 2) (2x – 3) + (5x – 3) (x + 1)

= 6x² – 9x – 4x + 6 + 5x² + 5x – 3x – 3

= 11x² – 11x + 3

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)