SOLUTION: Jack is mowing a lawn that has a shed. Jack wants to know the area of the lawn he has to mow. Dimensions of the yard are length 5x width 13x-4. The dimensions of the shed are lengt

Question 1107707: Jack is mowing a lawn that has a shed. Jack wants to know the area of the lawn he has to mow. Dimensions of the yard are length 5x width 13x-4. The dimensions of the shed are length 2x width 2x+4. Find a polynomial that describes the area of the lawn he has to mow. (i.e find the area of the yard minus the area of the shed.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the area of the yard is (5x) * (13x-4) = 65x^2 - 20x.

the area of the shed is (2x) * (2x+4) = 4x^2 - 8x.

the area of the yard minus the area of the shed is 65x^2 - 20x - 4x^2 - 8x.

combine like terms to get 61x^2 - 28x.

that's the polynomial that represents the area of the yard that needs to be mowed.

to test this out, replace x with a random value and solve both the original equation and the final equation to see if you get the same answer.

i let x = 5.

the final equation of 61x^2 - 28x becomes 61*5^2 - 28*5 = 1385 square units.

the original equation gets me (5x) * (13x-4) - (2x) * (2x+4) becomes (5*5) * (13*5-4) - (2*5) * (2*5+4).

this results in 1385 square units.

the answer is the same which indicates that the original equaiton and the final equation are identical.

this confirms the solution is good.

the solution is that your polynmoial that represents the area that needs to be mowed is 61x^2 - 28x.

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