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

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

Part 1: Polynomials multiplied by polynomials

Question 1 (a+b)X= ?

(a+b)X=aX+bX

When X=m+n, (a+b)X=?

(a+b)X=(a+b)(m+n)

Question 2 During the period of returning farmland to forest in a certain area, a rectangular forest area with an original length of m meters and a width of a meters grew by n meters and widened by b meters. Please indicate the current area of ​​this forest area.

Can you express the area of ​​the puzzle in a different way?

This forest area is now (m+n) meters long and (a+b) meters wide.

Since (m+n)(a+b) and (ma+mb+na+nb) represent the area of ​​the same land, there is:

(m+n)(a+b)=ma+ mb+ na+ nb.

How to multiply polynomials by polynomials?

In fact, considering (m+n) as a whole, we have:

(m+n)(a+b)= (m+n)a+(m+n)b

= ma+mb+na+nb.

Multiplication of integers PPT, part 2: analysis of examples

Example 1 calculation: (1) (1-x) (0.6-x); (2) (2x+y) (x-y);

Solution: (1) Original formula=1×0.6-1×x-x·0.6+x·x

=0.6－x－0.6x+x2

=0.6－1.6x+x2;

(2) Original formula=2x·x－2x·y+y·x－y·y

=2x2－2xy+xy－y2

=2x2-xy-y2;

(3) (x+y)(x2－xy+y2).

Solution: Original formula=x·x2－x·xy+xy2+x2y－xy2+y·y2

=x3－x2y+xy2+x2y－xy2+y3

= x3+y3.

Note: (1) missing multiplication; (2) sign problem; (3) the final result should be reduced to its simplest form (similar terms should be combined).

Example 2 Simplify first and then evaluate: (a-2b)(a2+2ab+4b2)-a(a-5b)(a+3b), where a=-1, b=1.

Solution: Original formula=a3-8b3-(a2-5ab)(a+3b)

=a3-8b3-a3-3a2b+5a2b+15ab2

=-8b3+2a2b+15ab2.

When a=-1, b=1, the original formula=-8+2-15=-21.

Method summary: When simplifying and evaluating questions, you must pay attention to simplifying first and then evaluating. You cannot substitute the value first and then calculate.

Multiplication of integers PPT, Part 3: Classroom exercises

1. Determine whether the following solution is correct. If it is wrong, please give the reason.

2. Calculate: (1)(x−3y)(x+7y); (2)(2x + 5y)(3x−2y).

3. Calculate and evaluate: (4x+3y)(4x-3y)+(2x+y)(3x-5y), where x=1, y=-2.

Multiplication of integers PPT, Part 4 content: Class summary

algorithm

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

(a+b)(m+n)=am+an+bm+bn

In essence, it is converted into the operation of monomial × polynomial

Notice

Do not miss multiplications; determine the symbols correctly; the results should be the simplest

(x-1)2=(x-1)(x-1), not x2-12.

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

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Update Time: 2024-09-26

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