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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