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"Multiplication Formula" Multiplication, division and factorization of integers PPT courseware 3
Activity 1 Knowledge Review
The rule for multiplying polynomials by polynomials: To multiply polynomials by 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.
Activity 2 Calculate the following questions. What patterns can you find?
(1) (x+1)(x－1); (2) (a+2)(a－2);
(3) (3-x)(3+x); (4) (2x+1)(2x-1).
Square difference formula:
(a+b)(a-b)=a2-b2.
That is, the product of the sum of two numbers and the difference between the two numbers is equal to the squared difference of the two numbers.
(-m+n) (-m-n) =m2-n2.
Activity 4 Practice
1. Are the following calculations correct? If it is wrong, how should it be corrected?
(1)(x+2)(x-2)=x2-2; (2)(-3a-2)(3a-2)=9a2-4.
2. Calculate using the square difference formula:
(1)(a+3b)(a - 3b)=
(2)(3+2a)(-3+2a)=
(3)(-2x2-y)(-2x2+y)=
(4)51×49=
(5)(3x+4)(3x-4)-(2x+3)(3x-2)=
Among the following polynomial multiplications, the ones that can be calculated using the square difference formula are ( ):
(1) (x+1)(1+x); (2) (a+b)(b-a);
(3)(-a+b)(a-b); (4)(x2-y)(x+y2);
(5)(-a-b)(a-b); (6)(c2-d2)(d2+c2).
Calculate using the square difference formula:
(1)(5+6x)(5－6x); (2)(x－2y)(x+2y);
(3)(-m+n)(-m-n).
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"Multiplication Formula" PPT:
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