I m always confused about the difference between the perfect square formula and the square formula,

The perfect square formula: (a+b) 2=a 2+2ab+b 2 (a b) 2=a 2 2ab+b 2

The squared difference formula: (a+b)(a b)=a 2 b 2 has three terms after the complete square formula, two square terms, and one double term, and this double term is twice the base of a 2 and b 2 (i.e., a, b); After the square difference formula is simplified, there are only two items, and both of these are square terms, which are the difference.

If this is too complicated, you can write it like this: after the complete square formula is simplified, there are many terms (there are three items), there is only one parentheses, a + b in the parentheses, and one square outside the parentheses; After the formula of square difference is simplified, the number of terms is small (there are two items), and there are two parentheses, one parenthesis in a+b, and the other in parentheses a b

I suggest you understand it literally.

First of all, both formulas come in two forms, one is integer multiplication and the other is factorization.

The perfect square formula is the sum or difference squared, then it has to be added or subtracted first, and then squared.

a+b)^2=a^2+2ab+b^2

a-b)^2=a^2-2ab+b^2

Whereas, the formula for square difference is that the sum of two numbers multiplied by the difference between these two numbers equals the square difference of these two numbers. Square first, then subtract.

a+b)(a-b)=a^2-b^2

Perfect Square Formula:

a +b)*(a+b)=(a+b)^2=a^2+2*a*b+b^2a - b)*(a - b)=(a-b)^2=a^2-2*a*b+b^2

Square Difference Formula:

a+b)*(a -b)=a^2-b^2

Summary: The perfect square formula is the multiplication of two identical terms to give three terms.

The squared difference formula multiplies two signs that are not exactly the same, and the result is two.

1. The formula is different.

Perfect square difference formula: (a-b) = a -2ab+b.

Squared difference formula: a -b = (a + b) (a-b).

2. The formula for calculating the exact square difference of the specific data is different (if a=2, b=1): (a-b) =a -2ab+b =1.

Square difference formula: a -b = (a + b) (a-b) = 3.

3. The meaning of the expression is different.

Perfect squared difference formula: The square of the difference between two numbers, equal to their sum of squares minus their product by 2 times.

Square Difference Formula: Refers to the product of the sum of two numbers and the difference between these two or muffled numbers, which is equal to the square difference of these two numbers.

These are two completely different formulas for different question types to solve.

Perfect squared difference formula: (a-b) = a -2ab + b square difference formula: (a+b)(a-b) = a -b.

The formula for squared difference is squared first and then subtracted a -b = a+b)(a-b).

The perfect square formula is first addition and subtraction, and finally squared (a b) = a 2ab+b.

The square difference formula refers to the product of the sum of two numbers and the difference between these two numbers, which is equal to the square difference of these two numbers

On the left is the multiplication of two binomials, one of which is exactly the same and the other is the opposite of each other; On the right is the square difference of the two terms in the multiplication, that is, the square difference between the square of the same term and the opposite term. The letters in a formula can represent specific numbers (positive and negative) or they can represent algebraic formulas such as monomials or polynomials.

The formula needs to be noted:

1.To the left of the equation is the product of two quadrats, one of which is identical.

2.The result on the right is the difference in the square of the two terms in the multiplication, the square of the same term minus the square of the opposite term.

3.a,b in a formula can be concrete numbers, or they can be mononomials or polynomials.

The perfect square formula refers to the sum (or difference) of two numbers squared, and the judgment is equal to their sum of squares, plus (or subtract) 2 times their product. For the sake of distinction, it will be called the perfect square formula of the sum of two numbers, or the perfect square formula of the difference between two numbers. Structural features of this formula:

1.On the left is the multiplication of two identical binomials, and on the right is the trinomial, which is the sum of the squares of the two terms in the binomial on the left, plus or minus 2 times the product of these two terms;

2.When the two symbols on the left are the same, the items on the right are connected by a "+" sign; When the two symbols on the left are opposite, the square term on the right is connected with a "+" sign and then doubled by the product of the two terms "-" (note: the term is not included here).

The letters in a formula can represent specific numbers (positive or negative) or mathematical formulas such as monomials or polynomials.

The formula needs to be noted:

1.On the left is a binomial perfectly squared.

2.On the right is the sum of the squares of the binomials, plus (or subtract) twice the product of these two terms, a and b are numbers, monomials, polynomials.

3.Whether it is (a+b)2 or (a-b)2, the last term is a plus sign, and don't take it for granted because of the previous symbol as the next symbol.

4.Don't miss the next item.

5.Never confuse the formula.

6.Do not make incorrect symbols in the calculation result.

7.Variant applications are difficult to fight and not easy to master.