Multiplying Polynomials Worksheet Algebra 1

Are you an algebra student seeking practice with multiplying polynomials? Look no further! This Multiplying Polynomials Worksheet for Algebra 1 is designed to provide you with ample opportunity to hone your skills in multiplying different types of polynomials.

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What is the product of x and y?

The product of x and y is xy.

Multiply (2x + 3)(x + 4).

To multiply (2x + 3)(x + 4), you use the distributive property. First, you multiply 2x by x and 2x by 4, then you multiply 3 by x and 3 by 4. This results in 2x^2 + 8x + 3x + 12, which simplifies to 2x^2 + 11x + 12. So the product of (2x + 3)(x + 4) is 2x^2 + 11x + 12.

Find the product of (7a - 2b)(3a + 5b).

To find the product of (7a - 2b)(3a + 5b), use the distributive property. (7a - 2b)(3a + 5b) = 7a * 3a + 7a * 5b - 2b * 3a - 2b * 5b. Simplifying this gives 21a^2 + 35ab - 6ab - 10b^2. Combining like terms, the final product is 21a^2 + 29ab - 10b^2.

Multiply (3x - 6)(x + 2).

To multiply (3x - 6)(x + 2), we use the distributive property. First, multiply 3x by x and 3x by 2 to get 3x^2 + 6x. Then, multiply -6 by x and -6 by 2 to get -6x - 12. Therefore, the product is 3x^2 + 6x - 6x - 12, which simplifies to 3x^2 - 12.

What is the result of (4x^2 + 5)(2x + 3)?

To find the result of (4x^2 + 5)(2x + 3), we use the distributive property to multiply each term in the first expression by each term in the second expression. This results in (4x^2 * 2x) + (4x^2 * 3) + (5 * 2x) + (5 * 3), which simplifies to 8x^3 + 12x^2 + 10x + 15. Therefore, the result is 8x^3 + 12x^2 + 10x + 15.

Multiply (2a + 3)(a^2 + 4a + 1).

To multiply (2a + 3)(a^2 + 4a + 1), distribute 2a to each term in the second parenthesis: 2a*a^2 + 2a*4a + 2a*1. Then, distribute 3 to each term in the second parenthesis: 3*a^2 + 3*4a + 3*1. Simplify the expression to get 2a^3 + 8a^2 + 2a + 3a^2 + 12a + 3, which simplifies further to 2a^3 + 11a^2 + 14a + 3.

Find the product of (5x - 2)(2x^2 + 3x - 1).

The product of (5x - 2)(2x^2 + 3x - 1) is 10x^3 + 15x^2 - 5x - 4x^2 - 6x + 2, which simplifies to 10x^3 + 11x^2 - 11x + 2.

Multiply (3a - 1)(2a^2 + 5a - 4).

The product of (3a - 1)(2a^2 + 5a - 4) is 6a^3 + 15a^2 - 12a - 2a^2 - 5a + 4 which simplifies to 6a^3 + 13a^2 - 17a + 4.

What is the product of (4x^2 - 3x + 2)(x^2 + 2x - 1)?

The product of (4x^2 - 3x + 2)(x^2 + 2x - 1) is 4x^4 + 8x^3 - 4x^2 - 3x^3 - 6x^2 + 3x + 2x^2 + 4x - 2, which simplifies to 4x^4 + 5x^3 - 7x^2 + 7x - 2.

Multiply (3a + 2)(a^3 - 4a^2 + 7a - 3).

To multiply (3a + 2)(a^3 - 4a^2 + 7a - 3), you can use the distributive property to multiply each term in the first parenthesis by each term in the second parenthesis. This results in the following multiplication: 3a * (a^3 - 4a^2 + 7a - 3) + 2 * (a^3 - 4a^2 + 7a - 3), which simplifies to 3a^4 - 12a^3 + 21a^2 - 9a + 2a^3 - 8a^2 + 14a - 6. Combining like terms gives the final answer: 3a^4 - 10a^3 + 13a^2 + 5a - 6.