In equilateral △ ABC, point P is in △ ABC, point q is outside △ ABC, and ∠ ABP = ∠ ACQ, BP = CQ. What shape of triangle is △ Apq? Try to state your conclusion

In equilateral △ ABC, point P is in △ ABC, point q is outside △ ABC, and ∠ ABP = ∠ ACQ, BP = CQ. What shape of triangle is △ Apq? Try to state your conclusion

In △ ABP and △ ACQ, ∵ AB = AC, ∵ AB = AC, ∵ AB = AC, ABP = acqbp = CQ, ≌ ABP ≌ ACQ (SAS). ∵ AP = AQ, ≌ BAP = CAQ. ∵ BAC = BAP + PAC = 60 °, PAQ = CAQ + PAC = 60 °, PAC = 60 °

Factorization
1、m²(m-1)-4(1-m)²
2、1-a²+ab-1/4b²
3、x³-x²y-xy²+y³
4、(x²+4x)²-8(x²+4x)+16
5、(x+2)(x-2)-4y(x-y)

Let's take apart the grouping decomposition method. Grouping decomposition is a simple method to solve equations. We can learn this knowledge. The equations that can be grouped and decomposed have four or more terms. Generally, there are two forms of grouping decomposition: dichotomy and Trinity. For example, ax + ay + BX + by = a (x + y) + B (x + y) = (a + b) (...)

n:0.0000001
The cube root of n is 0.01
n：0.001
The cube root of n is 0.1
n：1
The cube root of N: 1
n:1000
Cube root of N: 10
……
What is the law?

N is 1000 times larger and the cube root is 10 times larger

If we know that the image of the first-order function y = KX + B intersects with the positive scale function y = 13X at point a, and intersects with the y-axis at point B (0, - 4), point 0 is the origin of the coordinate, and the area of the triangle AOB is 6, then the analytic expression of the first-order function is______ ．

As shown in the figure, ∵ triangle AOB has an area of 6, ∵ 12a1e · ob = 6, ∵ ob = 4, ∵ a1e = 3, which is substituted into the positive proportion function y = 13X to get y = 1, that is, A1 (3, 1). Let the analytic expression of the first-order function be y = KX + B, then, − 4 = B1 = 3K + B, the solution is k = 53B = − 4, ∵ the analytic expression of the first-order function is y = 53x-4; similarly, another analytic expression of the first-order function is y = - x-4; so the answer is: y = - X- 4 or y = 53x-4