"Multiplication of Integers" Operations of Integers PPT Courseware 3

Description

"Multiplication of Integers" Operations of Integers PPT Courseware 3

teaching objectives

knowledge and abilities

1. The multiplication rule of integers;

2. Multiplication of monomials and polynomials;

3. Multiply polynomials with polynomials.

Process and Method

1. Experience the process of exploring the operational properties of multiplication of integers, further understand the meaning of power, and develop reasoning ability and organized expression ability;

2. Understand the operational properties of multiplication of integers and be able to solve some practical problems.

Emotional attitudes and values

1. Appreciate scientific thinking methods, accept the influence of mathematical culture, and inspire the spirit of exploration and innovation;

2. While developing reasoning ability and organized language and symbolic expression skills, further appreciate the interest in learning mathematics, improve the confidence in learning mathematics, and feel the simplicity and beauty of mathematics;

3. Go through the process of exploring the multiplication rules of integers, gain successful experience, accumulate rich mathematical experience, and penetrate the simple beauty and harmonious beauty of mathematical formulas.

Knowledge points

To multiply a monomial by a monomial, multiply their coefficients and the same letters respectively. For letters contained in only one monomial, use its exponent as a factor of the product.

Rules for multiplying monomials and monomials:

(1) Multiply the coefficients of each monomial;

(2) The powers of the same letters are multiplied respectively;

(3) A letter contained only in a monomial factor, together with its exponent, serves as a factor of the product.

practice

(1) (2xy2)·(xy)

(2) (-2a2b3)·(-3a)

(3) (4×106)·(5×107)

(4)x2y3·(-xy2)2

When a monomial is multiplied by a polynomial, there are three stages:

① According to the distributive law of multiplication, write the product as the algebraic sum of the product of a monomial and a monomial;

② Multiplication operation of monomials;

③Add the resulting products.

Notice

1. The result of multiplying a monomial by a polynomial is still a polynomial, and the number of terms in the product is the same as the number of terms in the original polynomial.

2. When multiplying a monomial by each term of a polynomial, pay attention to the determination of the sign of each term of the product: multiplication with the same sign is positive, multiplication with different signs is negative.

3. Don’t miss out on multiplication, and operations must be done in order.

practice

(-2ab)3(5a2b–2b3)

Solution: Original formula =(-8a3b3)(5a2b–2b3)

=(-8a3b3)·(5a2b)+(-8a3b3)·(-2b3)

=-40a5b4+16a3b6

Explanation: First perform the exponentiation operation, and then perform the multiplication operation of monomials and polynomials.

Knowledge points

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

(1) Multiply each term of one polynomial by each term of another polynomial. Do not miss multiplications. Before merging similar terms, the number of terms after the two polynomials are multiplied and expanded should be the number of terms of the original two polynomials. product.

(2) Each term in the polynomial must be a signed monomial.

(3) After expansion, there are similar items that need to be merged and reduced to the simplest form.

Class summary

1. When using the multiplication rules of polynomials, you must ensure that there are no repetitions or omissions.

2. Multiplying polynomials with polynomials still yields polynomials.

3. Pay attention to determine the sign of each term in the product. Each term in the polynomial contains the sign before it. "Same signs result in positive, different signs result in negative".

4. In the expansion of polynomials and multiplication of polynomials, if there are similar terms, similar terms should be combined.

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For more information about the PPT courseware "Multiplication of Integers and Operations of Integers", please click the Multiplication of Integers ppt Operations of Integers ppt tag.

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Update Time: 2024-10-03

This template belongs to Mathematics courseware Beijing Normal University seventh grade mathematics volume 2 industry PPT template

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