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1. Simplify: 5n(2n3+n2+8)+n(4-n).Solution:5n(2n3+n2+8)+n(4-n).= 5n × 2n3 + 5n × n2 + 5n × 8 + n × 4 - n × n.= 10n4 + 5n3 + 40n + 4n – n2.= 10n4 + 5n3 + 44n – n2.= 10n4 + 5n3 – n2 + 44n.Answer: 10n4 + 5n3 – n2 + 44n
2. Simplify: 4y(y2-8y+6)-3(2y3-5y2+2)Solution:
4y(y2-8y+6)-3(2y3-5y2+2).= 4y3 - 32y2 + 24y – 6y3 + 15y2 – 6.= 4y3 – 6y3 - 32y2 + 15y2 + 24y – 6.= -2y3 – 17y2 + 24y – 6.Answer: -2y3 – 17y2 + 24y – 63. Find the area, diameter = 12m.

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Solution:
Diameter = 12 meter.Radius = diameter/2.= 12/2.= 6 meter.Area of a one = πr2.Here, pi (π) = 3.14 meter, radius (r) = 6.Area that a one = 3.14 × 6 × 6.. = 3.14 × 36. = 113.04 square meter or 113.04 m2.Answer: 113.04 square meter or 113.04 m24. Find the area, radius = 8cm.Solution:Given, Radius = 8 cm.Area the a one = πr2.Area that a one = 3.14 × 8 × 8 . = 3.14 × 64. = 200.96 square cm or 200.96 cm2.Answer: 200.96 square centimeter or 200.96 cm2.5. Simplify: 4x2(x+2)+3x(5x2+2x-6)-5(3x2-4x).Solution:4x2(x+2) +3x(5x2+2x-6) -5(3x2-4x).= 4x3 + 8x2 + 15x3 + 6x2 – 18x – 15x2 + 20x.= 4x3 + 15x3 + 8x2 + 6x2 – 15x2 – 18x + 20x.= 19x3 - x2 + 2x.Answer: 19x3 - x2 + 2x6. Factoring with recurring of the distinction of square formula. Element the answer completely.3y4 – 3u4y4.Solution:3y4 – 3u4y4.= 3y4(1 – u4).= 3y4(1 – (u2)2).= 3y4(1 + u2)( 1 - u2) .= 3y4(1 + u2)( 1 + u) ( 1 - u).Answer: 3y4(1 + u2)( 1 + u) ( 1 - u).7. Factoring with recurring of the difference of square formula. Variable the prize completely.u4x3 – 81x3.Solution:u4x3 – 81x3.= x3(u4 – 81).= x3((u2)2 – 92).= x3(u2 + 9)(u2 – 9).= x3(u2 + 9)(u2 – 32).= x3(u2 + 9)(u + 3)(u – 3).Answer: x3(u2 + 9)(u + 3)(u – 3).8. Factoring with repetitive of the distinction of square formula. Aspect the prize completely.2w2 – 2v4w2.Solution:2w2 – 2v4w2.= 2w2 (1 – v4).= 2w2 (1 – (v2)2).= 2w2 (1 + v2)(1 - v2).= 2w2 (1 + v2)(1 + v)(1 – v).Answer: 2w2 (1 + v2)(1 + v)(1 – v).9. Factoring with repetitive of the difference of square formula. Aspect the prize completely.3u2x4 – 48u2.Solution:3u2x4 – 48u2.= 3u2(x4 – 16).= 3u2((x2)2 – 42).= 3u2(x2 +4)(x2 – 4).= 3u2(x2 +4)(x2 – 22).=3u2(x2 +4)(x + 2)(x – 2).Answer: 3u2(x2 +4)(x + 2)(x – 2).10. Factoring a amount or difference of 2 cubes. Factor: 64 + u3.Solution:64 + u3.= 43 + u3.= (4 + u)(42 – 4.u + u2).= (4 + u)(16 – 4u + u2).Answer: (4 + u)(16 – 4u + u2)11. Factoring a amount or distinction of 2 cubes. Factor: 125 - 8u3Solution:125 - 8u3.= 53 – (2u)3.= (5 – 2u)(52 + 5.2.u + (2u)2 ).= (5 – 2u)(25 + 10u + 4u2).Answer: (5 – 2u)(25 + 10u + 4u2)12. Fixing a linear equation v several incidents of the variable, resolve for w. Leveling your prize as much as possible.(7w + 6)/6 + (9w +8)/2 = 22Solution:(7w + 6)/6 + (9w +8)/2 = 22or, <7w + 6 + 3(9w + 8)>/6 = 22or, 7w + 6 + 27w + 24 = 132or, 34w + 30 = 132or, 34w = 132 - 30or, 34w = 102or, w = 102/34Therefore, w = 3Answer: w = 313. Find the worth of p: 2p+8p-6=7p+2pSolution:2p + 8p - 6 = 7p + 2por, 10p – 6 = 9por, 10p – 6 – 9p = 9p – 9por, ns – 6 = 0or, p - 6 + 6 = 6Therefore, ns = 6.Answer: ns = 614. Simplify: (24sp)/(3s)Solution:(24sp)/(3s).= 8p.Answer: 8p15. Rewrite 3/8 as a decimalSolution:3/8 is a fraction; we require to change 3/8 to decimal number by dividing.

Answer: 0.375

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