Help with Math Problems
Math Only Math is there to help with math problems from basic to intricate problems. Care has been taken to help with math problems in such a way that students can understand each and every step.
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 – 6
3. Find the area, diameter = 12m.
Solution:
Diameter = 12 meter.
Radius = diameter/2.
= 12/2.
= 6 meter.
Area of a circle = πr2.
Here, pi (π) = 3.14 meter, radius (r) = 6.
Area of a circle = 3.14 × 6 × 6..
= 3.14 × 36.
= 113.04 square meter or 113.04 m2.
Answer: 113.04 square meter or 113.04 m2
4. Find the area, radius = 8cm.
Solution:
Given, Radius = 8 cm.
Area of a circle = πr2.
Area of a circle = 3.14 × 8 × 8 [We know, pi (π) = 3.14].
= 3.14 × 64.
= 200.96 square cm or 200.96 cm2.
Answer: 200.96 square cm 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 + 2x
6. Factoring with repeated of the difference of square formula. Factor the answer completely.
3y4 – 3u4y4.
Solution:
3y4 – 3u4y4.
= 3y4(1 – u4).
= 3y4(1 – (u2)2).
= 3y4(1 + u2)( 1 - u2) [since we know a2 – b2 = (a + b)(a – b)].
= 3y4(1 + u2)( 1 + u) ( 1 - u).
Answer: 3y4(1 + u2)( 1 + u) ( 1 - u).
7. Factoring with repeated of the difference of square formula. Factor the answer 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 repeated of the difference of square formula. Factor the answer 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 repeated of the difference of square formula. Factor the answer 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 sum or difference of two 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 sum or difference of two cubes.
Factor: 125 - 8u3
Solution:
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. Solving a linear equation with several occurrences of the variable, solve for w. Simplify your answer as much as possible.
(7w + 6)/6 + (9w +8)/2 = 22
Solution:
(7w + 6)/6 + (9w +8)/2 = 22
or, [7w + 6 + 3(9w + 8)]/6 = 22
or, 7w + 6 + 27w + 24 = 132
or, 34w + 30 = 132
or, 34w = 132 - 30
or, 34w = 102
or, w = 102/34
Therefore, w = 3
Answer: w = 3
13. Find the value of p: 2p+8p-6=7p+2p
Solution:
2p + 8p - 6 = 7p + 2p
or, 10p – 6 = 9p
or, 10p – 6 – 9p = 9p – 9p
[Subtract 9p from both the sides]
or, p – 6 = 0
or, p - 6 + 6 = 6
[Add 6 to both the sides]
Therefore, p = 6.
Answer: p = 6
14. Simplify: (24sp)/(3s)
Solution:
(24sp)/(3s).
= 8p.
Answer: 8p
15. Rewrite 3/8 as a decimal
Solution:
3/8 is a fraction; we need to change 3/8 to decimal number by dividing.
Answer: 0.375
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