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Mastering Monomials and Polynomials: A Step-by-Step Guide to Simplification

This educational resource will help students gain a firm understanding of how to multiply monomials with polynomials effectively. With clear objectives and a series of simplification challenges, learners will practice using the distributive property and combining like terms. Step-by-step examples cover various expressions, including multiplying variables with exponents and applying the distributive property to simplify complex polynomials. Ideal for classroom reinforcement or individual study at Varina High School, this guide encourages mastery of algebraic concepts.

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Mastering Monomials and Polynomials: A Step-by-Step Guide to Simplification

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  1. ObjectivesThe student will be able to: 1. multiply a monomial and a polynomial. SOL: A.2b Designed by Skip Tyler, Varina High School

  2. Review: When multiplying variables, add the exponents! 1) Simplify: 5(7n - 2) Use the distributive property. 5 • 7n 35n - 10 - 5 • 2

  3. 2) Simplify: 6a2 + 9a 3) Simplify:6rs(r2s - 3) 6rs • r2s 6r3s2 - 18rs - 6rs • 3

  4. 4) Simplify: 4t2(3t2 + 2t - 5) + 8t3 - 20t2 12t4 5) Simplify: - 4m3(-3m - 6n + 4p) 12m4 + 24m3n - 16m3p

  5. 6) Simplify: (27x2 - 6x + 12) 16x3 - 28x2 + 4x Fooled ya, didn’t I?!? Ha! Ha! Here’s the real answer! -9x3 + 2x2 - 4x

  6. Simplify 4y(3y2 – 1) • 7y2 – 1 • 12y2 – 1 • 12y3 – 1 • 12y3 – 4y

  7. Simplify -3x2y3(y2 – x2 + 2xy) • -3x2y5 + 3x4y3 – 6x3y4 • -3x2y6 + 3x4y3 – 6x2y3 • -3x2y5 + 3x4y3 – 6x2y3 • 3x2y5 – 3x4y3 + 6x3y4

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