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Introduction to Multiplying and Simplifying Polynomials

Learn how to multiply and simplify polynomials, rewrite into standard form, identify missing terms, leading coefficients, constant terms, and degrees. Includes examples and step-by-step explanations.

mitchelljames
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Introduction to Multiplying and Simplifying Polynomials

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  1. Intro to Polynomials I will be able to multiply and simplify polynomials LT: • Rewrite into standard form • What are the missing terms? • What is the leading coefficient? • What is the constant term? • List the degrees • What is the degree of the polynomial? Today’s Agenda Success Criteria • I can multiply a polynomials • I can simplify • Do Now • Lesson • HW#23

  2. Multiplying Polynomials By Monomials When multiplying, 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. 4(d2 + 5d) + d(d2 – 7d + 2) 7) 4y(y2 – 8y + 6) – 3(2y3 – 5y2 + 2)

  6. Multiplying Polynomials We use the distributive property to multiply two or more polynomials. • Distribute the first term of the first ( ) to ALL terms in the second ( ). • Distribute the second term of the first ( ) and continue until you are done with the first ( ). • Combine like terms.

  7. 1. ( x – 5)( x + 7) x2 + 7x – 5x – 35 x2 + 2x – 35

  8. 2. (2x + 3)(5x + 8) 10x2 + 16x + 15x + 24 10x2 + 31x + 24

  9. 3. (3x – 5)(5x + 2) 15x2 + 6x – 25x – 10 15x2 – 19x – 10

  10. 4. (7p – 2)(3p – 4) 21p2 – 28p – 6p + 8 21p2 – 34p + 8

  11. 5. (a – 3)(a2 – 8a + 5) a3 – 8a2 + 5a – 3a2 + 24a – 15 a3 – 11a2 + 29a – 15

  12. 6. (3c + 2)(c2 – 4c + 8) 3c3 – 12c2 + 24c + 2c2 – 8c + 16 3c3 – 10c2 + 16c + 16

  13. HW#23

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