Consider the difference of squares a² - b², for integer values of a and b. Part A Make a table of the difference of squares using consecutive integers for a and b. What pattern do you notice? Part B Use the pattern from Part A to find pair of consecutive integers that generates a difference of squares of -45. Part C Make a table of the difference of squares using consecutive even integers for a and b. What pattern do you notice? Part D Use the pattern from Part C to find a pair of consecutive even integers that generates a difference of squares of -100.

Consider a rectangle with length x and width y. The area, A, of the rectangle is A=. The perimeter of the rectangle, P, is P=. If the perimeter of the rectangle is 180 inches, then y=. Substituting this expression for y in the formula for area, the area of the rectangle can be expressed as A(x)=.

Show that a positive integer is the difference of two squares if and only if it is not of the form 4k + 2, where k is an integer.

The expression 96² - 95² is a difference of two squares. How can you use the factors (96 - 95)(96 + 95) to make it easier to simplify this expression?

Find each product. (x + 9) (x + 9) , (x - 7)(x - 7) (2x - 1 )² a. What do all products of the square of a binomial have in common? b. Will the third term of the square of a binomial always be positive? Explain. c. what is the relationship between the sign of the binomial and the sign of the second term in the product? d. What is true about the exponents representing perfect square variables?

A large indoor market is set up with 4 rows of booths. There are large booths with an area of x² sq. units, medium booths with an area of x sq. units, and small booths with an area of 1 sq. unit. In the marketplace, two of the rows contain 7 large booths, 6 medium booths, and 5 small booths each. The other two rows each contain 3 large booths, 5 medium booths, and 10 small booths. What is the total area of the booths in the marketplace?

consider the following set of monomials. A = {2x, 3x, 4x, 5xy, 7x, 9y, 12xy, 13x, 15x} The GCF the elements in subset B = {2x, 3x} is x. Create 6 different subsets of A, such the GCFs of the elements are 1, 2x, 3, 4x, 5x, and y.

Use the square of a binomial to find each product. 56²

Write the factored form of each trinomial. x² + 18xy + 45y²

It is possible to write any positive integer as the sum of powers of 2 with whole number exponents. For example, you can write 75 in the following manner.

$$2^0 + 2^1 + 2³ + 2^6 = 75$$

Part A Use the equation above to write 75 as the sum of powers of 8, using rational exponents. What are possible values for a, b, c and d?

$$8^a + 8^b + 8^c+ 8^d= 75$$

Part B How can you modify the equation you wrote in part A to express 75 as sum of powers of 16?

$$16^a + 16^b + 16^c + 16^d = 75$$

Part C Given that a, b, c, and d are rational numbers, for what types of integer values of x is the following equation true? Explain your answer.

$$x^a + x^b + x^c + x^d = 75$$

What would be the dimensions of the larger wall area you would need if you used 11 of the 1 ft-by-1 ft units while keeping the other units the same?

Ella is a landscape photographer. One weekend at her gallery she sells a total of 52 prints for a total of $2,975. How many of each size print did Ella sell? Small print:$50 Large print: $75

Each side of a triangle lies along a line in a coordinate plane. The three lines that contain these sides are represented by the given equations. Equation 1: x - 2y = -4, Equation 2: 2x + y = -3, Equation 3: 7x - 4y = 12 Part A Write three systems of equations that can be used to determine the vertices of the triangle. Part B What are the coordinates of the vertices? Part C Is this a right triangle? Explain.

Factor each trinomial completely. 9x² + 46x + 5