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Can someone please help me on this? I've been trying to figure this out for about 20 minutes now but I don't know how to do it.

Part A: The area of a square is (16x2 + 24x + 9) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)

Part B: The area of a rectangle is (4x2 − 49y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

2 Answers

2 votes

Answer:

Explanation:

Part A: The length of each side of the square is (4x + 3).

My work for Part A:

Step 1: Check for a GCF: There is no GCF. We can move on to Step 2.

Step 2: Split the middle term by multiplying the leading coefficients, finding a factor that adds to the middle term, then replace those factors with the middle term: 16 x 9 = 144, and 12 and 12 is a factor of 144 that adds to 24. (16x2 + 12x + 12x + 9).

Step 3: Factor by grouping: 4x(4x + 3) 3(4x + 3).

Step 4: Rewrite the expression by only writing the common binomial once and using the factors outside the parentheses in another parentheses together: (4x + 3) (4x + 3).

Step 5: Since it is a square all sides are the same length, so you only need one expression: (4x + 3).

Part B: The dimensions of the rectangle are (2x + 7y) and (2x – 7y).

My work Part B:

Step 1: Determine whether the binomial is a difference of two squares: The expression must have two terms, check! Both of which are perfect squares, check! They are separated by a subtraction sign, check! This expression is the difference of perfect squares!

Step 2: Find the square root of each term and then place them in the difference of two square patterns which is (a + b) (a – b): The square root of 4 is 2, and the square root of 49 is 7.

(2x + 7y) (2x – 7y).

User Feuby
by
7.3k points
4 votes
Hello,

A)
16x^2+24x+9=(4x)^2+2*4x*3+3^2=(4x+3)^2\\

B)
4x^2-49y^2=(2x)^2-(7y)^2=(2x-7y)(2x+7y)
User Namenlos
by
8.5k points