"Formula Method: Complete Square Formula" Multiplication and factorization of integers PPT

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"Formula Method: Complete Square Formula" Multiplication and factorization of integers PPT

Part One: Knowledge Review

What methods have we learned about factoring?

Common factor method: pa+pb+pc=p(a+b+c)

Formula method: squared difference formula method:

In addition to the squared difference formula, what other formulas have you learned?

think

Can you factor these two polynomials?

That is, the square of two numbers plus (or subtracting) 2 times the two numbers is equal to the square of the sum (or difference) of the two numbers.

This method of factoring is called factoring using the perfect square formula.

Formula method of perfect square formula PPT, the second part of the content: understanding of the formula

The left side of the formula is the polynomial to be decomposed (perfect square method)

Features: The three terms have the same square sign and the middle term has twice the value

The right side of the formula is the result of decomposition

Features: The square of the sum or difference has the same sign

Completely flat judgment

Only the perfect square method can be used to decompose factors using the perfect square formula.

So how to judge whether an expression is completely square?

Formula method of perfect square formula PPT, the third part of the content: induction

Steps to factor using the perfect square formula:

1. Observe the coefficient of the square term. If it is negative, ________ first.

2. Change the formula into the form of ____________.

3． Factoring.

Things to note when factoring using the perfect square formula:

1. The symbol in the middle after decomposition is _________ before decomposition.

2. After decomposition, the items in parentheses correspond to the items under _______.

Formula method of perfect square formula PPT, the fourth part: formula method

By exchanging the positions of both sides of the equal sign of the multiplication formula, you can get the formula for factoring, which is used to factor certain polynomials with special forms. This method of factoring is called the formula method.

Factoring steps

1. First observe whether there is ________. If there is a common factor, extract the common factor first.

2. Observe the number of items after extraction:

If there are two items, consider using the ______________ formula.

If there are three items, consider using the ______________ formula.

Of course, it is possible that it cannot be decomposed anymore.

3． Check if it is possible to ______________.

Formula method of perfect square formula PPT, the fifth part: summary

What did we learn in this lesson?

How to judge whether an expression is completely square?

1. Number of items to look at: must be 3 items

2. Look at the square: the signs before the square must be the same

3． Look at the product. It must be twice the number or formula of two squares.

By exchanging the positions of both sides of the equal sign of the multiplication formula, you can get the formula for factoring, which is used to factor certain polynomials with special forms. This method of factoring is called the formula method.

Factoring steps

1. First observe whether there is ________. If there is a common factor, extract the common factor first.

2. Observe the number of items after extraction:

If there are two items, consider using the ______________ formula.

If there are three items, consider using the ______________ formula.

Of course, it is possible that it cannot be decomposed anymore.

3． Check if it is possible to ______________.

PPT courseware for the first volume of eighth-grade mathematics published by the People's Education Press can be downloaded for free, PPT download of the perfect square formula of the formula method, PPT download of the multiplication and factorization of integers, in .PPT format;

For more information about the PPT courseware "Perfect Square Formulas for Multiplication and Factorization of Integers", please click on the PPT tag of "Perfect Square Formulas for Multiplication and Factorization of Integers".

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Update Time: 2024-07-02

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 1 industry PPT template

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