Question

Subtract the expressions. Show or explain at least two steps of your process.

(3y2-4y+5)-(4y2+2y-9)

Multiply the two binomials. Show or explain at least two steps of your process.

(5x-8) (3x+1)

Multiply the two polynomials. Show or explain at least two steps of your process.

(a-2) (2a2-5a+8)

Dubay’s Pool Company sells rectangular in-ground pools of any size as long as the width is twice the length of the pool. They also provide cement walkways around their pools that are always 4 feet wide all the way around. Find the surface area of the cement walkway for any given pool. Show or explain how you find the simplified expression.

To help get you started:
Outside Area= length*width= (2x+8)(x+8) multiply these together
Pool Area= length*width = (2x)(x)
Subtract the areas.

Factor the expression. Show or explain at least two steps of your process.

x2-5x-24

Factor the expression. Show or explain at least two steps of your process.

x2-36

Answer 1

Algebra gives the result of each of the following expressions as follows;

1) -y^2 - 2y - 4

2) 15x^2 - 19x - 8

3) 2a^3 - 9a^2 +  18a - 16

4) 24x + 64

5) (x + 3) (x - 8)

6) (x - 6) (x + 6)

What is an expression?

The term expression refers to a mathematical statement that lacks the equality sign. Now let us answer the questions individually;

1) In order to subtract (3y2-4y+5)  from (4y2+2y-9), we must remove the brackets to have and collect like terms;

3y^2-4y+5 - 4y^2+2y-9

3y^2 - 4y^2 -4y +2y +5 -9

-y^2 - 2y - 4

2) to multiply the polynomials, we have;

(5x-8) (3x+1)

15x^2 + 5x - 24x - 8

15x^2 - 19x - 8

3) This multiplication gives;

(a-2) (2a^2-5a+8)

2a^3 - 5a^2 + 8a - 4a^2 + 10a - 16

Collecting like terms

2a^3 - 5a^2  - 4a^2 + 8a + 10a - 16

2a^3 - 9a^2 +  18a - 16

4) The product is;

(2x+8)(x+8)

2x^2 + 16x + 8x + 64

2x^2 + 24x + 64

Hence;

2x^2 + 24x + 64 - 2x^2

24x + 64

5) The expression is; x^2-5x-24

x^2 -8x + 3x - 24

x(x - 8) +3(x - 8)

(x + 3) (x - 8)

6) The expression x^2-36 represents difference of two squares hence;

x^2 - 6^2

(x - 6) (x + 6)

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