"Multiplication of Integers" PPT on Multiplication and Division of Integers (Lesson 2)

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"Multiplication of Integers" PPT on Multiplication and Division of Integers (Lesson 2)

Part One: Multiplying Monomials and Polynomials

Rule for multiplying monomials by polynomials

To multiply a monomial by a polynomial, multiply the monomial by each term of the polynomial and add the resulting products.

Note: (1) The basis is the distributive law of multiplication;

(2) The number of terms of the product is the same as the number of terms of the polynomial.

Example 1 Calculation:

(1) 2ab(5ab2+3a2b);

(3) 5m2n(2n+3m-n2);

(4) 2(x+y2z+xy2z3)·xyz;

Example 2 A flood control dam has a trapezoidal cross-section with a meter width at the top and bottom.

The lower base is (a+2b) meters wide and the dam is a meter high.

(1) Find the cross-sectional area of ​​the flood control dam;

(2) If the flood control dam is 100 meters long, what is the volume of this section of flood control dam in cubic meters?

Example 3 Simplify first and then evaluate: 5a(2a2-5a+3)-2a2(5a+5)+7a2, where a=2.

Summary of method: When calculating, pay attention to simplifying first and then calculating the value.

The addition and subtraction operations of integers are actually removing parentheses and merging similar terms.

Multiplication of integers PPT, Part 2: Classroom exercises

1. Multiplying a monomial and a polynomial means multiplying the _________ of the polynomial by the monomial, and then _________ the resulting product.

2.4(a-b+1)=____________.

3.3x（2x-y2）=____________.

4. (2x-5y+6z)(-3x)=______________.

5.(-2a2)2(-a-2b+c)=_______________.

6. Calculate:

(1) (-4x)·(2x2+3x-1);

7. Calculate: -2x2·(xy+y2)-5x(x2y-xy2).

8. Simplify first, and then evaluate 3a(2a2-4a+3)-2a2(3a+4), where a=-2.

Solution: 3a(2a2-4a+3)-2a2(3a+4)

=6a3-12a2+9a-6a3-8a2

=-20a2+9a.

When a=-2, the original formula =-20×(-2)2+9×(-2)=-98.

Multiplication of integers PPT, part 3: Class summary

Multiply a monomial by a polynomial

In essence, it is converted into monomial × monomial

Notice

(1) When calculating, pay attention to the sign issue. Each term in the polynomial includes the sign before it. When the monomial is multiplied by each term of the polynomial, the multiplication with the same sign will be positive, and the multiplication with different signs will be negative.

(2) Don’t miss out on multiplication

(3) Operations must be in order: first exponentiation, then multiplication and division, and finally addition and subtraction

(4) For mixed operations, note that similar items should be merged at the end

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"Multiplication of Integers" PPT download of multiplication and division of integers (Lesson 2):

"Multiplication of Integers" Multiplication and Division of Integers PPT Download (Lesson 2) Part One Content: Learning Objectives 1. Be able to explore the rules for multiplying monomials and polynomials based on the distributive law of multiplication and the rules for multiplying monomials and polynomials; (Key Points) 2 .Master monomials and polynomials..

"Multiplication of Integers" PPT download of multiplication and division of integers (Lesson 1):

"Multiplication of Integers" Multiplication and Division of Integers PPT Download (Lesson 1) Part One Content: Learning Objectives 1. Master the operation rules of multiplying monomials and monomials. (Key Points) 2. Be able to flexibly perform operations of multiplying monomials and monomials. (Difficulty) ... ... ...

"Multiplication of Integers" Multiplication and Division of Integers PPT (Lesson 3):

"Multiplication of Integers" Multiplication and Division of Integers PPT (Lesson 3) Part 1: Problem of multiplying polynomials by polynomials 1 (a+b)X= ? (a+b)X=aX+bX When X=m+n (a +b)

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Update Time: 2024-11-24

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