"Polynomials Multiplied by Polynomials" PPT courseware 2

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"Polynomials Multiplied by Polynomials" PPT courseware 2

Review & Thoughts

How to multiply monomials and polynomials?

① Multiply the monomial by each term of the polynomial

② Add the resulting products

What should you pay attention to when multiplying monomials and polynomials?

① No missing multiplications: that is, the monomial must be multiplied by every term of the polynomial

② Pay attention to the symbols when removing brackets.

situational navigation

The car starts from Beijing, travels at a speed of a km/h, and arrives in Tianjin after t hours. Then, the car speed increases by b kilometers/hour compared with the original, and the driving time is w hours longer than Beijing to Tianjin to reach Mount Tai. How many kilometers is the journey from Tianjin to Mount Tai?

Thinking: Taking a car from Tianjin to Mount Tai,

The driving speed is (a+b) kilometers/hour,

The time taken is (t+w) hours,

The stroke is (a+b)(t+w).

Discussion: How to calculate (a+b)(t+w)?

Consider (a+b) as a whole, we have:

(a+b)(t+w)=(a+b)t + (a+b)w

= at+aw+bt+bw

think:

What are the issues that need to be paid attention to when multiplying polynomials by polynomials?

Notice:

1. There must be no duplication or omission.

2. Pay attention to determine the sign of each term in the product.

3. The result should be reduced to the simplest form {merging similar terms}.

Summary

Rules for multiplying polynomials by polynomials:

To multiply polynomials, first multiply each term of one polynomial by each term of the other polynomial, and then add the resulting products.

Notice:

1. There must be no duplication or omission.

2. Pay attention to determine the sign of each term in the product.

3. The result should be reduced to its simplest form.

Expand and extend

Simplify and evaluate: given y=2, find the algebraic formula

(y+2)·(y2-2y+1)-y·(y2+1).

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"Polynomials Multiplied by Polynomials" PPT courseware recall 1. The rule of multiplying a monomial by a monomial 2. The rule of multiplying a monomial by a polynomial If they are regarded as four small rectangles, then their areas can be expressed as _____, _____, _____, _____ respectively. If Take a look at it..

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Update Time: 2024-06-14

This template belongs to Mathematics courseware Qingdao Edition Seventh Grade Mathematics Volume 2 industry PPT template

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