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

Answer:

$Area = x^2- 25$

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

$Length = (3x -2)$

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

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

Step-by-step 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

$Area = Length * Width$

$Length = \frac{Area}{Width}$

$Length = \frac{3x^2 + 7x - 6}{x + 3}$

Factorize the numerator

$Length = \frac{3x^2 + 9x -2x - 6}{x + 3}$

$Length = \frac{3x(x + 3) -2(x + 3)}{x + 3}$

$Length = \frac{(3x -2) (x + 3)}{x + 3}$

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:

$Speed = \frac{Distance}{Time}$

$Speed = \frac{2y^3 - 7y^2 + 5y -1}{2y - 1}$

Factorize the numerator

$Speed = \frac{\left(2y-1\right)\left(y^2-3y+1\right)}{2y - 1}$

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

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

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

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

Answer 2

Answer:

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