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.

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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