A gardener wants to create a rectangular garden with length of 8x - 4y ft. and width of 5x + 9y ft. What is an algebraic expression for the area of the garden?
(8x-4y)*(5x+9y)=5x*8x-5x*4y+9y*8x-9y*4y=
40x^2-20xy+72xy-36y^2=
40x^2+52xy-36y^2
To find the area of the garden, you need to multiply the length by the width.
The length of the garden is given as 8x - 4y ft.
The width of the garden is given as 5x + 9y ft.
Therefore, the algebraic expression for the area of the garden can be obtained by multiplying the length and the width:
Area = (8x - 4y) * (5x + 9y)
To simplify this expression, you can use the distributive property of multiplication:
Area = 8x * 5x + 8x * 9y - 4y * 5x - 4y * 9y
Simplifying further, you can multiply the terms:
Area = 40x^2 + 72xy - 20xy - 36y^2
Combining like terms, you get:
Area = 40x^2 - 20xy + 72xy - 36y^2
Finally, you can simplify it to get the simplified expression for the area of the garden:
Area = 40x^2 + 52xy - 36y^2