Multiplying Polynomials Worksheet Answer Key

In need of a reliable and comprehensive resource to help you practice multiplying polynomials? You've come to the right place! This blog post offers an extensive collection of worksheets with an answer key, specifically designed for individuals seeking to strengthen their skills in multiplying polynomials. With a focus on clarity and accuracy, each worksheet will provide a valuable opportunity for you to develop a deeper understanding of this fundamental mathematical concept.

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  Factoring Cubic Polynomials

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What is the answer to (x + 5) * (2x - 3)?

The answer to (x + 5) * (2x - 3) is 2x^2 + 7x - 15.

Expand and simplify the expression (3a + 2b) * (4a - 5b).

To expand and simplify the expression (3a + 2b) * (4a - 5b), you need to distribute the terms in the first bracket to the terms in the second bracket. This will result in: 3a * 4a + 3a * -5b + 2b * 4a + 2b * -5b. Simplifying this further, we get 12a^2 - 15ab + 8ab - 10b^2, which simplifies to 12a^2 - 7ab - 10b^2.

Multiply the polynomials (x^2 + 3x + 2) * (2x - 1).

To multiply the polynomials (x^2 + 3x + 2) * (2x - 1), you would first distribute each term in the first polynomial by each term in the second polynomial. This would result in the following: x^2 * 2x + x^2 * (-1) + 3x * 2x + 3x * (-1) + 2 * 2x + 2 * (-1). Simplifying each term gives 2x^3 - x^2 + 6x^2 - 3x + 4x - 2. Combining like terms further simplifies it to 2x^3 + 5x^2 + x - 2. Therefore, the result of multiplying the given polynomials is 2x^3 + 5x^2 + x - 2.

Simplify the product of (2x^2 + 5x + 3) * (x - 2).

The simplified product of (2x^2 + 5x + 3) * (x - 2) is 2x^3 - 4x^2 + 5x^2 - 10x + 3x - 6, which simplifies to 2x^3 + x^2 - 7x - 6.

Find the result of multiplying (3x - 2) * (4x^2 + 1).

To find the result of multiplying (3x - 2) by (4x^2 + 1), you can use the distributive property. Multiply each term in the first polynomial by each term in the second polynomial and then combine like terms. (3x - 2) * (4x^2 + 1) simplifies to 12x^3 - 8x^2 + 3x - 2.

Expand and simplify (2a^2 + 3b) * (a - b^2).

Expanding (2a^2 + 3b) * (a - b^2) will result in 2a^3 - 2a^2b + 3ab - 3b^3 after simplifying.

Multiply the binomials (5x + 2) * (3x - 1).

To multiply the binomials (5x + 2) and (3x - 1), you would use the distributive property. Multiply each term in the first binomial by each term in the second binomial, and then combine like terms. The result of (5x + 2) * (3x - 1) simplifies to 15x^2 + 5x - 6.

Simplify the product of (2x^2 + 4x + 1) * (x - 3).

To simplify the product of (2x^2 + 4x + 1) * (x - 3), you can apply the distributive property. Multiply each term in the first expression by each term in the second expression. This gives you: 2x^2 * x + 4x * x + 1 * x - 3 * 2x^2 - 3 * 4x - 3 * 1. Simplifying these terms gives you: 2x^3 + 4x^2 + x - 6x^2 - 12x - 3. Finally, combine like terms to get the simplified result: 2x^3 - 2x^2 - 11x - 3.

Calculate (4a^2 - 3a + 2) * (a + 1).

To calculate (4a^2 - 3a + 2) * (a + 1), you need to distribute each term of the first expression (4a^2 - 3a + 2) by each term of the second expression (a + 1) and then simplify the resulting expression. The result after simplification would be 4a^3 + a^2 - 3a^2 - 3a + 2a + 2, which simplifies to 4a^3 - 2a^2 - a + 2.

Find the value of (x^3 + 2x^2 + x) * (3x + 2) when x = 2.

Substitute x = 2 into the expression (x^3 + 2x^2 + x) * (3x + 2) to get (2^3 + 2*2^2 + 2) * (3*2 + 2) = (8 + 8 + 2) * (6 + 2) = 18 * 8 = 144. Therefore, the value of the expression when x = 2 is 144.