[PDF] Find each product. 1. (x + 5)(x + 2) SOLUTION: 2. (y

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Find each product.

(x + 5)(x + 2) (y 2)(y + 4) (b 7)(b + 3) (4n + 3)(n + 9) (8h 1)(2h 3) (2a + 9)(5a 6) Hugo is designing a frame as shown. The frame has a width of x inches all the way around. Write an expression that represents the total area of the picture and frame. The total length is 2x + 20 and the width is 2x + 16.

Find each product.

(2a 9)(3a2 + 4a 4) (4y2 3)(4y2 + 7y + 2) (x2 4x + 5)(5x2 + 3x 4) (2n2 + 3n 6)(5n2 2n 8)

Find each product.

(3c 5)(c + 3) (g + 10)(2g 5) (6a + 5)(5a + 3) (4x + 1)(6x + 3) (5y 4)(3y 1) (6d 5)(4d 7) (3m + 5)(2m + 3) (7n 6)(7n 6) (12t 5)(12t + 5) (5r + 7)(5r 7) (8w + 4x)(5w 6x) (11z 5y)(3z + 2y)

A walkway surrounds a rectangular garden. The width of the garden is 8 feet, and the length is 6 feet.

The width x of the walkway around the garden is the same on every side. Write an expression that represents the

total area of the garden and walkway.

Let 2x + 8 = the width of the garden and walkway and let 2x + 6 = the length of the garden and walkway.

Find each product.

(2y 11)(y2 3y + 2) (4a + 7)(9a2 + 2a 7) (m2 5m + 4)(m2 + 7m 3) (x2 + 5x 1)(5x2 6x + 1) (3b3 4b 7)(2b2 b 9) (6z2 5z 2)(3z3 2z 4)

Simplify.

(m + 2)[(m2 + 3m 6) + (m2 2m + 4)] [(t2 + 3t 8) (t2 2t + 6)](t 4)

CCSS STRUCTURE

Find the area of the circle.

Find the area of the rectangle.

Subtract the area of the rectangle from the area of the circle. The area of the shaded region is represented by the expression 4x2 + 12x + 9 3x2 5x 2.

Find the area of the rectangle.

Find the area of the triangle.

Subtract the area of the triangle from the area of the rectangle. The area of the shaded region is represented by the expression 24x2 . The dimensions of a sand volleyball court are represented by a width of 6y 5 feet and a length of 3y + 4 feet. Write an expression that represents the area of the court. The length of a sand volleyball court is 31 feet. Find the area of the court. a. The area of the court is represented by the expression 18y2 + 9y 20. b.

Substitute 9 for y in the expression for area to find the area of the sand volleyball court when the length is 31 feet.

The area of the sand volleyball court is 1519 ft2. Write an expression for the area of a triangle with a base of 2x + 3 and a height of 3x 1. The area of the triangle is represented by the expression .

Find each product.

(a 2b)2 (3c + 4d)2 (x 5y)2 (2r 3t)3 (5g + 2h)3 (4y + 3z)(4y 3z)2

What are the possible values of x? Explain.

Which shape has the greater area?

What is the difference in areas between the two?

The value of x must be greater than 4. If x = 4 the width of the rectangular sandbox would be zero and if x < 4

the width of the rectangular sandbox would be negative. b.

The square has the greatest area.

c. Subtract the area of the rectangle from the area of the square.

The difference in the areas is 4 ft2.

In this problem, you will investigate the square of a sum.

Copy and complete the table for each sum.

Make a conjecture about the terms of the square of a sum. For a sum of the form a + b, write an expression for the square of the sum. a.

The first term of the square of a sum is the first term of the sum squared. The middle term of the sum is two

times the first term of the sum multiplied by the last term of the sum. The third term of the square of the sum is the

last term of the sum squared. Then, Determine if the following statement is sometimes, always, or never true. Explain your reasoning. The FOIL method can be used to multiply a binomial and a trinomial.

Always; by grouping two adjacent terms, a trinomial can be written as a binomial (the sum of two quantities), and

apply the FOIL method. For example, (2x + 3)( x2 + 5x + 7) = (2x + 3)[ x2 + (5x + 7)] = 2x(x2) + 2x(5x + 7) + 3

(x2) + 3(5x + 7). Then use the Distributive Property and simplify.

Find (xm + x p)(xm1 x1p + xp).

Write a binomial and a trinomial involving a single variable. Then find their product.

Sample answer: x 1, x2 x 1.

Compare and contrast the procedure used to multiply a trinomial by a binomial using the vertical method with the procedure used to multiply a three-digit number by a two-digit number.

The three monomials that make up the trinomial are similar to the three digits that make up the 3-digit number. The

single monomial is similar to a 1-digit number. With each procedure you perform 3 multiplications. The difference is

that polynomial multiplication involves variables and the resulting product is often the sum of two or more monomials,

while numerical multiplication results in a single number.

Consider the following examples.

Summarize the methods that can be used to multiply polynomials.

The Distributive Property can be used with a vertical or horizontal format by distributing, multiplying, and combining

like terms.

The FOIL method is used with a horizontal format. You multiply the first, outer, inner, and last terms of the binomials

and then combine like terms.

A rectangular method can also be used by writing the terms of the polynomials along the top and left side of a

rectangle and then multiplying the terms and combining like terms.

What is the product of 2x 5 and 3x + 4?

5x 1

6x2 7x 20

6x2 20

6x2 + 7x 20

Choice B is the correct answer.

Which statement is correct about the symmetry of this design?

The design is symmetrical only about the y-axis.

The design is symmetrical only about the x-axis.

The design is symmetrical about both the y- and the x-axes.

The design has no symmetry.

Consider each choice.

For the design to be symmetrical only about the y-axis, you can fold it along the y-axis. The part to the right and

left of the y-axis should be identical. In this case they are. So the figure is symmetrical about the y-axis.

For the x-axis, you can fold it on the x-axis. The part above and below the x- axis, should be identical. In this case they are not. So it is not symmetrical about the x-axis. Since the figure is not symmetrical about the x-axis, you can eliminate this choice.

Since the figure is symmetrical about the y-

Thus, Choice F is the correct answer.

Which point on the number line represents a number that, when cubed, will result in a number greater than itself?

P Q R T

Choice D is the correct answer.

For a science project, Jodi selected three bean plants of equal height. Then, for five days, she measured their heights in centimeters and plotted the values on the graph below. She drew a line of best fit on the graph. What is the slope of the line that she drew? The line passes through the points (1, 1) and (5, 7).

So, the slope of the line is .

Carrie has $6000 to invest. She puts x dollars of this money into a savings account that earns 2%

interest per year. She uses the rest of the money to purchase a certificate of deposit that earns 4% interest. Write an

equation for the amount of money that Carrie will have in one year. Let x = the amount placed into the 2% interest savings account Let 6000-x = the amount placed into the 4% certificate of deposit

To calculate the amount of money that will be in the account at the end of the year, use principle (1 + rate)

(The 1 + the rate will add back in the original money deposited.)

Savings account:

Certificate of deposit:

Therefore, T = 1.02x + 1.04(6000 x)

Find each sum or difference.

(7a2 5) + (3a2 + 10) (8n 2n2) + (4n 6n2) (4 + n3 + 3n2) + (2n3 9n2 + 6) (4u2 9 + 2u) + (6u + 14 + 2u2) (b + 4) + (c + 3b 2) (3a3 6a) (3a3 + 5a) (4m3 m + 10) (3m3 + 3m2 7) (3a + 4ab + 3b) (2b + 5a + 8ab)

Simplify.

(2t4)3 3(2t3)4 (3h2)3 2(h3)2

2(5y3)2 + (3y3)3

3(6n4)2 + (2n2)2

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18-3 Multiplying Polynomials

Find each product.

(x + 5)(x + 2) (y 2)(y + 4) (b 7)(b + 3) (4n + 3)(n + 9) (8h 1)(2h 3) (2a + 9)(5a 6) Hugo is designing a frame as shown. The frame has a width of x inches all the way around. Write an expression that represents the total area of the picture and frame. The total length is 2x + 20 and the width is 2x + 16.

Find each product.

(2a 9)(3a2 + 4a 4) (4y2 3)(4y2 + 7y + 2) (x2 4x + 5)(5x2 + 3x 4) (2n2 + 3n 6)(5n2 2n 8)

Find each product.

(3c 5)(c + 3) (g + 10)(2g 5) (6a + 5)(5a + 3) (4x + 1)(6x + 3) (5y 4)(3y 1) (6d 5)(4d 7) (3m + 5)(2m + 3) (7n 6)(7n 6) (12t 5)(12t + 5) (5r + 7)(5r 7) (8w + 4x)(5w 6x) (11z 5y)(3z + 2y)

A walkway surrounds a rectangular garden. The width of the garden is 8 feet, and the length is 6 feet.

The width x of the walkway around the garden is the same on every side. Write an expression that represents the

total area of the garden and walkway.

Let 2x + 8 = the width of the garden and walkway and let 2x + 6 = the length of the garden and walkway.

Find each product.

(2y 11)(y2 3y + 2)quotesdbs_dbs12.pdfusesText_18

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