Question

Learning Task 3:

Solve.
1. What is the area of the rectangle whose length is (x + 5) and width (x - 5)?
2. What is the area of the square whose sides measure (3x + 4)?
3. The area of the rectangle is 3x2 + 7x - 6, what is the length if the width is
(x + 3)
4. What is the average speed of the car that covers a distance of
(2y3-7y2 + 5y - 1) km in (2y-1) hour?
5. Multiply (m2 + 2m-2) by the sum of (m + 3 ) and (2m - 3)​

Answer 1

Step-by-step explanation:

Solving (1):

Required

Calculate Area

Solving (2):

Given

Required: Calculate Area

Solving (3):

Required: Calculate Length

Factorize the numerator

Divide by x + 3

Solving (4):

Required: Determine the average speed

This is calculated as:

Factorize the numerator

Solving (5):

Multiply by sum of and

First, calculate the sum:

Then, the product

Answer 2

`Area = x^2- 25`

`Area =9x^2 +24x + 16`

`Length = (3x -2)`

`Speed = \left(y^2-3y+1\right)`

`Product = 3m^3 + 6m^2 - 6m`

Explanation:

Solving (1):

`Length = (x + 5)`

`Width = (x - 5)`

Required

Calculate Area

`Area = Length * Width`

`Area = (x + 5) * (x - 5)`

`Area = x^2 + 5x - 5x - 25`

`Area = x^2- 25`

Solving (2):

Given

`Length = (3x + 4)`

Required: Calculate Area

`Area =Length * Length`

`Area =(3x + 4) * (3x + 4)`

`Area =9x^2 + 12x + 12x + 16`

`Area =9x^2 +24x + 16`

Solving (3):

`Area = 3x^2 + 7x - 6`

`Width = x + 3`

Required: Calculate Length

`Area = Length * Width`

`Length = (Area)/(Width)`

`Length = (3x^2 + 7x - 6)/(x + 3)`

Factorize the numerator

`Length = (3x^2 + 9x -2x - 6)/(x + 3)`

`Length = (3x(x + 3) -2(x + 3))/(x + 3)`

`Length = ((3x -2) (x + 3))/(x + 3)`

Divide by x + 3

`Length = (3x -2)`

Solving (4):

`Distance = (2y^3 - 7y^2 + 5y -1)`

`Time = 2y - 1`

Required: Determine the average speed

This is calculated as:

`Speed = (Distance)/(Time)`

`Speed = (2y^3 - 7y^2 + 5y -1)/(2y - 1)`

Factorize the numerator

`Speed = (\left(2y-1\right)\left(y^2-3y+1\right))/(2y - 1)`

`Speed = \left(y^2-3y+1\right)`

Solving (5):

Multiply
`(m^2 + 2m - 2)` by sum of
`(m + 3)` and
`(2m - 3)`

First, calculate the sum:

`Sum = m + 3 + 2m - 3`

`Sum = m + 2m+3 - 3`

`Sum = 3m`

Then, the product

`Product = (m^2 + 2m - 2)(3m)`

`Product = 3m^3 + 6m^2 - 6m`