Middle School Math Formulas 40, Middle School Math Formulas

a2-b2=(a+b)(a-b) a3+b3=(a+b)(a2-ab+b2) a3-b3=(a-b(a2+ab+b2)

Trigonometric inequality |a+b|≤|a|+|b| |a-b|≤|a|+|b| |a|≤b<=>-b≤a≤b

a-b|≥|a|-|b| -a|≤a≤|a|

Solution of a quadratic equation -b+ (b2-4ac) 2a -b- (b2-4ac) 2a

Relation of root to coefficient x1+x2=-b a x1*x2=c a Note: Veda's theorem.

1 Multiplication and factoring.

a＋b)(a－b)＝a2－b2；

a±b)2＝a2±2ab＋b2；③(a＋b)(a2－ab＋b2)＝a3＋b3；④(a－b)(a2＋ab＋b2)＝a3－b3；a2＋b2＝(a＋b)2－2ab；(a－b)2＝(a＋b)2－4ab。

The nature of the operation to the power of 2.

am×an＝am+n；

am÷an＝am-n；

am)n＝amn；

ab)n＝anbn；

4 Trigonometric inequalities|a|-|b|≤|a±b|≤|a|+|b|(Theorem); Reinforcement conditions: ||a|-|b||≤a±b|≤|a|+|b|Also established.

This inequality can also be referred to as the trigonometric inequality of vectors (where a and b are vectors a and b, respectively).

5 The sum of the first n terms of certain sequences.

1+2+3+4+5+6+7+8+9+…+n=n(n+1)/2；1+3+5+7+9+11+13+15+…+2n-1)=n2 ；Brother Jing 2 + 4 + 6 + 8 + 10 + 12 + 14 +...+2n)=n(n+1)；

12+22+32+42+52+62+72+82+…+n2=n(n+1)(2n+1)/6；13+23+33+43+53+63+…n3=n2(n+1)2/4；

1*2+2*3+3*4+4*5+5*6+6*7+…+n(n+1)=n(n+1)(n+2)/3；

6 Unary quadratic equations for equations:

ax2 bx c 0: where b2 4ac is called the discriminant of the root.

When 0, the equation has two unequal real roots;

When 0, the equation has two equal real roots;

When 0 shines silver, the equation has no real roots Note: When 0, the equation has real roots.

If the equation has two real roots x1 and x2, then the quadratic trinomial ax2 bx c can be decomposed into a(x x1) (x x2).

The unary quadratic equation with a and b as the root is x2 (a b) x ab 0.

7 The image of the primary function y kx b(k≠0) is a straight line (b is the ordinate of the intersection of the line and the y-axis, called the intercept).

When k is 0, y increases with x (straight line rises from left to right);

When k 0, y decreases as x increases (straight line descends from left to right);

In particular, when b 0, y kx (k≠0) is also called a proportional function (y is proportional to x), and the image must pass through the origin.