Grade 9 Algebra: Please Help!, Multiply Polynomial Expressions

Question

A tennis court is surrounded by a fence so that the distance from each boundary (edge) of the tennis court to the fence is the same. If the tennis court is 75 feet long and 30 feet wide, then the dimensions of the fence would be (2x+75) and (2x+30) feet.

What is the expression for area of the entire surface inside the fence?

Answer 1

This is basic FOIL

(2x + 75)(2x + 30)

= (2x)(2x) + (2x)(30) + (2x)(75) + (75)(30)

= 4x^2 + 60x + 150x + 2250

= 4x^2 + 210x + 2250

Answer 2

Here is a great opportunity to review both F-O-I-L and long multiplication.

1) What is (ax+b)(cx+d) ? [use F-O-I-L)

acx² + adx + bcx + bd

So, (2x+75)(2x+30) is

4x² + 60x + 150x + 2250

4x² + 210x + 2250

2) 2x + 75

times 2x + 30

-----------------

60x ⁺ 2250

4x² + 150x

---------------------------

4x² + 210x + 2250

Note: MATH is built very strongly on prerequisites, so always consider what you have already learned.