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Multiplying Binomials and Polynomials

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Multiplying Binomials and Polynomials

Use the distributive property to multiply each expression. Combine like terms and show your working. All answers should be written in standard form.

Expand the Robot-Base Dimensions

Sofia is designing rectangular bases for the club’s robots. Each side length is an algebraic expression. Find each area by multiplying the side lengths.

1.Find the area of a base with side lengths (x + 2) and (x + 3). Expand and simplify.

2.Find the area of a second base with side lengths (x - 4) and (x + 2). Expand and simplify.

3.Which expression is the correct expansion of (a + 5)(a - 2)?

a² + 3a - 10
a² - 3a + 10
a² + 7a - 10
2a² + 3a

Power Up with Distribution

A robot’s control panel uses expressions with more than two terms. Multiply every term in the first factor by every term in the second factor, then collect like terms.

4.Logan expands (w - 8)(w + 5). Write the two distributed products, then simplify the final answer.

5.Multiply (y - 1)(y² + 7y - 2). Write your answer in descending powers of y.

6.Expand (2x - 3)(x² + 4x - 1).

7.Find the product (3a + 2)(2a² - a + 4).

8.Choose the expression equal to (2x - 1/3)(x + 3/2).

2x² + 8x/3 - 1/2
2x² + 3x - 1/2
2x² - 8x/3 - 1/2
2x² + 8x/3 + 1/2

9.A student claims (p + 4)(p - 4) = p² + 16. Is the claim correct? Explain the sign error and give the correct product.

Debug and Design

Check your expansion carefully: distribute to every term, then combine only like terms.

10.Aaliyah writes (x + 2)(x² - 3x + 5) = x³ - 3x² + 5x + 2. Identify what went wrong and write the correct expansion.

11.A rectangular robot platform has side lengths (x + 6) inches and (x + 1) inches. Write a simplified polynomial for its area. Then find the area when x = 2.