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).