"Polynomials Multiplied by Polynomials" PPT courseware

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"Polynomials Multiplied by Polynomials" PPT courseware

remember

1. Rule for multiplying monomials by monomials

2. Rules for multiplying monomials by polynomials

If they are regarded as four small rectangles, then their areas can be expressed as _____, _____, _____, _____ respectively.

If it is regarded as a large rectangle, then its side lengths are _____, _____, and its area can be expressed as _________.

(a+b)(c+d)==ac+bc+ad+bd

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

Example 1 Calculation:

(1) (x+2y)(5a+3b);

(2) (2x–3)(x+4) ;

Solution: (x+2y)(5a+3b)

=x ·5a +x ·3b +2y ·5a +2y ·3b

=5ax+3bx+10ay+6by

Solution: (2x–3)(x+4)=2x2 +8x –3x –12

=2x2+5x–12

Note: In the results of multiplying polynomials and polynomials, similar terms must be combined.

Did you notice?

When polynomials are multiplied by polynomials, the number of terms after expansion is very regular. Before combining similar terms, the number of terms in the expansion is exactly equal to the product of the terms of the two polynomials.

Several issues that need attention

1. Missed multiplication

2. Symbol problem

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

Notice !

1. Calculating (2a+b)2 should be done like this:

(2a+b)2=(2a+b)(2a+b)

=4a2+2ab+2ab+b2

=4a2+4ab+b2

Remember that generally

(2a+b)2 is not equal to 4a2+b2.

2. (3a–2)(a–1)–(a+1)(a+2) is the product of polynomials and the difference between the products. The expansion of the product of the last two polynomials should be enclosed in parentheses.

3. (x+y)(2x–y)(3x+2y) is the multiplication of three polynomials. You should choose two of them to multiply first, enclose their product in parentheses, and then multiply with the third one. .

Keywords: Teaching courseware for multiplying polynomials by polynomials, Qingdao edition seventh grade mathematics second volume PPT courseware download, seventh grade mathematics slide courseware download, multiplying polynomials by polynomials PPT courseware download, .PPT format;

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"Polynomials Multiplied by Polynomials" PPT Courseware 2:

"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 ..

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Update Time: 2024-06-25

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

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