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