Try Some of These Math Problems and Show how to work them?

Question

1. Add: (6f^5 + 8f^3 - 8) + (5f^5 - 3f + 8)

2. Subtract: (x^2 + 2x - 5) - (-7x^2 - 3x - 4)

3. Multiply: (x - 3) (x^2 + 2x + 4)

Answer 1

1. Add: (6f^5 + 8f^3 - 8) + (5f^5 - 3f + 8)=

        11f^5 +8f^3 -3f

2. Subtract: (x^2 + 2x - 5) - (-7x^2 - 3x - 4)=

x^2 + 2x - 5 +7x^2 + 3x + 4=

8x^2 +5x -1

3. Multiply: (x - 3) (x^2 + 2x + 4)=

x  (x^2 + 2x + 4)= x^3 +2x^2 +4x

- 3 (x^2 + 2x + 4)=-3x^2 -6x -12

now add them and get x^3  -x^2 -2x -12

Answer 2

1.

Remove brackets - (you can't add x^3 and x^2, only like terms like 2x^2 and x^2 can be added. The power of your variable, here f, must be same for two terms to be added)

6f^5 + 8f^3 - 8 + 5f^5 - 3f + 8

Rearrange -

= 6f^5 + 5f^5 + 8f^3 - 3f - 8 + 8

= (6+5)f^5 + 8f^3 - 3f.

= 11f^5 + 8f^3 - 3f.

2.

Remove brackets -

x^2 + 2x - 5 + 7x^2 + 3x + 4

Rearrange - (because of the - sign before the bracket, take the opposite of each sign present inside the bracket)

= x^2 + 7x^2 + 2x + 3x - 5 + 4

= (7+1)x^2 + 5x -1

= 8x^2 + 5x -1

3. Multiply the numbers in the second bracket with each number in the first.

x(x^2 + 2x + 4) - 3(x^2 + 2x + 4)

= x^3 + 2x^2 + 4x - 3x^2 - 6x - 12

= x^3 - x^2 + 4x - 12

Answer 3

To add polynomials, just combine like terms.

1.

6f^5 + 5f^5 + 8f^3 - 3f + 8 - 8

11f^5 + 8f^3 - 3f

To subtract polynomials, take the opposite of everything after the subtract sign, and add the result to the first polynomial

2.

(x^2 + 2x - 5) + (7x^2 + 3x + 4)

8x^2 + 5x - 1

To multiply polynomials, multiply every term in the first one with every term in the second one and combine like terms.

3.

x(x^2) + x(2x) + x(4) - 3(x^2) - 3(2x) - 3(4)

x^3 + 2x^2 + 4x - 3x^2 - 6x - 12

x^3 - x^2 - 2x - 12

Answer 4

you can only add and subtract like terms

you cannot add terms with x squared in them and terms with x cubed in them - it is like saying you have 3 apples and 2 oranges

you can say you have five fruits but not five apples or five bananas

for #3 you multiply each of the three terms in the second bracket by x, and the each term in the second bracket by minus 3, and then you collect like terms and simplify your answer

3. is x³ + 2x² + 4x    minus ( 3x² + 6x + 12)

so x³ - x² -2x -12

Answer 5

1) you can only add like terms so

  6f^5 + 8f^3 - 8

+5f^5 -  3f   + 8

  11f^5 + 8f^3 - 3f

2)you can only subtract like terms

  x^2 + 2x -5

+7x^2 +3x +4             (distribute the - to make it an addition prob.)

  8x^2 +5x -1

3) you use the distributive property for this one

x*x^2 +x*2x +x*4 -(3*x^2 +3*2x +3*4) multiply

x^3 + 2x^2 + 4x - 3x^2 - 6x - 12 combines like terms

x^3 - x^2 -2x -12