Calculation of 3 * (4 + 1) * (4 & sup2; + 1) with square difference formula

Calculation of 3 * (4 + 1) * (4 & sup2; + 1) with square difference formula

3 * (4 + 1) * (square of 4 + 1)
=(4-1) * (4 + 1) * (square of 4 + 1)
=(square of 4-1) * (square of 4 + 1)
=The fourth power of 4-1
=256-1
=255

Square difference formula: - N & sup2; + (M + n) & sup2; 2

Original formula = (M + N + n) (M + N-N)
=m(m+2n)

Factorization of 1 (a + B + C) & sup2; - (a + B-C) & sup2; 22ab & sup3; - 2Ab 34 (2P + 3Q) & sup2; - (3p-q) & sup2;
Pay attention,

1 (a+b+c)²-(a+b-c)² =(a+b+c+a+b-c)(a+b+c-a-b+c)=(2a+2b)(2c)=4c(a+b)2 2ab³-2ab=2ab(b²-1)=2ab(b+1)(b-1)3 4(2p+3q)²-(3p-q)² =(4p+6q)²-(3p-q)²=(4p+6q+3p-q)(4p+6q-3p...

758 & sup2; - 258 & sup2; calculated by factorization

758²-258²
=(758+258)(758-258)
=1016*500
=508000

Calculating 758 & sup2; - 258 & sup2 by factorization;

758²-258²
=(758+258)(758-258)
=1016*500
=508000

How to do (a + b) & sup2; - (a-b) & sup2; (using the square difference formula)

Take a + B A-B as a whole, (a + b) & sup2; - (a-b) & sup2; = (a + B + a-b) (a + B-A + b) = 2A * 2B = 4AB

Factorization prime factor
The teacher uses 216 yuan to buy a pen. If each pen is one yuan cheaper, he can buy three more pens. Question: how much is each pen?
Come on

It can be analyzed in this way
Suppose 216 can buy a pen originally, and each pen costs B yuan, then AB = 216
Each pen is one yuan cheaper, buy three more, then (a + 3) (B-1) = 216
So there is: 3B = a + 3, that is: a = 3b-3
That is to say, a is about three times as much as B
So: 216 = ab ≈ 3B & # 178;
8²

What is the factorization prime factor?

That is: write a number as the product of several prime numbers
For example:
12=2×2×3
75=5×5×3

It's best to have an example

25=5*5
Because decomposing prime factor means decomposing a composite number into the form of multiplication of several prime numbers, the number 25 to be decomposed should be written on the left side of the equal sign, and the product form to be decomposed should be written on the right side of the equal sign
Decomposing prime factor: each composite number can be written in the form of multiplication of several prime numbers, in which each prime number is the factor of the composite number, which is called the prime factor of the composite number. To express a composite number in the form of multiplication of prime factors is called decomposing prime factor

The factorization prime factor is______ ．

The prime factor of 28 is 28 = 2 × 2 × 7, so the answer is 28 = 2 × 2 × 7