1. Quadratic power of X (x + 1) - quadratic power of Y (Y-1) + XY 2.p(p+1)(p-1)-q(q+1)(q-1)

1. Quadratic power of X (x + 1) - quadratic power of Y (Y-1) + XY 2.p(p+1)(p-1)-q(q+1)(q-1)

1. Quadratic power of X (x + 1) - quadratic power of Y (Y-1) + XY
=x²(x+1)-y²(y-1)+xy
=x³+x²-y³+y²+xy
=x³-y³+x²+xy+y²
=(x-y)(x²+xy+y²)+x²+xy+y²
=(x²+xy+y²)(x-y+1)
2.p(p+1)(p-1)-q(q+1)(q-1)
=p(p²-1)-q(q²-1)
=p³-p-q³+q
=p³-q³-p+q
=(p-q)(p²+pq+q²)-(p-q)
=(p-q)(p²+pq+q²-1)

Factorization in junior one
(3x+2y)²-3x(3x-4y)=_______
[（a-4)(a+4+6)+3(a+4)]×2+(a+4)×1=___________
Detailed problem solving process ~)

1. The original formula = 9x & sup2; + 12xy + 4Y & sup2; - 9x & sup2; + 12xy = 4Y & sup2; 2. The original formula = [(A-4) (a + 10) + 3A + 12] * 2 + A + 4 = (A & sup2; + 10a-4a-40 + 3A + 12) * 2 + A + 4 = (A & sup2; + 9a-28) * 2 + A + 4 = 2A & sup2; + 18a-56 + A + 4 = 2A & sup2; + 19a-52

3x·x-5x-12
2x·x·x-x·x-4x+3
x·x·x-6x-5
x·x+6x+6
4x·x+12x+7

For example, suppose (x + a) (x + b) = x * x + 6x + 6, then the equation can be decomposed into a factorization with radical. There is a common method in junior high school mathematics before the factorization, cross multiplication. The specific operation steps can be

(1) What's the product of 2 / 3 plus 1 / 5 divided by 3 / 4?
(2) The investment of factory a is 500000 yuan, which is 2 / 3 of that of factory B, and that of factory C is 4 / 5 of that of factory B. how much is the investment of factory C (3) the turnover of a supermarket in the first half of December is 9.6 million yuan, which is 4 / 4 less than that in the second half. How much is the turnover of this supermarket in December?

(1) (2 / 3 + 1 / 5 △ 3 / 4) × 5 / 4 = 7 / 6 [7 / 6] (2) according to the title, Party B invested 50 △ 2 / 3 = 75, while Party C invested 75 × 4 / 5 = 100; (3) according to the title, the second half of December is 960 △ 1-1 / 4 = 1280, so the business volume in December is 960 + 1280 = 2240

In the middle of a circle is a square composed of four triangles. The area of a triangle is 8 cm. Find the area of the outer circle!

What four triangles are congruent or not congruent? If congruent, the answer is 8 π

The solution of 4x-3x (20-x) = 5x-7x (20-x)

4x-60x+3x*x=5x-140x+7x*x
4x*x-79x=0
x(4x-79)=0
X = 0 or x = 79 / 4

The circumference of a semicircle is 25 or 7 decimeters. How many square decimeters is its area?

Simple calculation of 128 × 32

128×32
＝125×32＋3×32
＝125×8×4＋3×32
＝4000＋96
＝4096

In △ ABC, ∠ BAC = 120 °, ab = 2, AC = 1, D is a point on the edge BC, then the value range of vector ad multiplied by vector BC

Do you want a closed interval or an open interval? If D can coincide with B or C, it is a closed interval, otherwise it is an open interval
First of all, let me give you a conclusion: let ad = XAB + YAC, then: x + y = 1 ------ if you need proof, please let me know
BC = ac-ab, then: ad · BC = (XAB + YAC) · (- AB + AC) = - x | ab | ^ 2 + y | AC | ^ 2 + (X-Y) ab · AC
=-4x+y+(x-y)*2*1*cos(2π/3)=-4x+y-(x-y)=2y-5x=2y-5(1-y)=7y-5,0≤y≤1
So: ad · BC ∈ [- 5,2], when point d coincides with point C, the maximum value of ad · BC is 2
When point d coincides with point B, the minimum value of ad · BC is - 5

How to solve: (a-b) (A2 AB B2) = a3-b3

(a-b)(a^2+ab+b^2)=a^3-b^3
This is the formula of cubic difference