Urgent!!! Solve a few problems with the common factor method

1,（x+y-z)(x-y+z)-(y+z-x)(z-x-y)（x+y-z)(x-y+z）+（y+z-x)(x+y-z)(x+y-z)(x-y+z+y+z-x)

2z(x+y-z)

2,2xy+3 y²

y(2x+3y)

x-square+2xy+y-square=(x+y) The common factor method cannot be used.

3, ax-bx=x(a-b) and by-ay=-y(a-b) have a common factor (a-b).

The square of 6 xy + 8 x y = 2xy(3+4x), 4x-3=-(4x+3) has a common factor of 4x+3

ab-ac=a(b-c) ab-bc=b(a-c) has no common factor.

a-b) 3x and (b-a) squared y have a common factor (a-b).

1 Put the negative sign in (z-x-y) is (x+y-z), so the common factor is (x+y-z).

2xy+3+y^2

3 There is no common factor y

4x-3 of 3 does not have a common factor x

(1) 4 power of x - 2 power of x.

x²(x²-1)

x²(x+1)(x-1)

2) xy-9x to the power of 3 y

xy(1-9x²)

xy(1+3y)(1-3y)

3) 2nd power of a (x+y) - 3rd power of 4a and 2nd power c = a [(x+y) -4c].

a³(x+y+2c)(x+y-2c)

4) 2nd power (x-y) of 4a + 2nd power (y-x) of b = 4a (x-y)-b (x-y).

x-y)(4a²-b²)

x-y)(2a+b)(2a-b)

5) 4 (a-b) to the 2nd power - (a+b) to the 2nd power = (2a-2b + a+b) (2a-2b-a-b) = (3a-b) (a-3b).

6) (x to the power of 2 + x + x + 1) to the power of 2 - 1

x²+x+1+1)(x²+x+1-1)=(x²+x+2)(x²+x)

x(x+1)(x²+x+2)

7) x to the 2nd power - 6x+9

x-3) 8)9(x+y) to the 2nd power -6(x+y)+1=[3(x+y)-1].

3x+3y-1)²

9) (2nd power of a + 2nd power of b) - 2nd power of 4a = (a + b + 2 ab) (a + b -2 ab) = (a + b ) (a-b) (a-b).

10) 5mx to the 2nd power - 10mxy + 5my to the 2nd power = 5m (x - 2xy + y).

5m(x-y)²

11) -2a to the 3rd power b to the 2nd power + 8a to the 2nd power b to the 2nd power - 8ab to the 2nd power.

2ab²(a²-4a+4)

2ab²(a-2)²

12) 4 (x + y) to the 2nd power + 25-20 (x + y) = [2 (x + y) - 5].

2x+2y-5)²

13) (a+2b) to the 2nd power - 8a (a + 2b) + 16a to the 2nd power = (a + 2b - 4a).

a-2b)²

14）（x+2）（x-6）+16

x²-4x-12+16

x²-4x+4

x-2) 15)-a to the power of 2 +81

(a²-9)

(a+9)(a-9)

16) 9y to the 3rd power - 4y

y(9y²-4)

y(3y+2)(3y-2)

17) 4A to the 2nd power + 4AB+B to the 2nd power.

2a+b)²

18) x to the 4th power -1

x²+1)(x²-1)

x²+1)(x+1)(x-1)

19) 2nd power of ay - 2nd power of 2a y + 3rd power of a = a (y - 2ay + a).

a(y-a)²

20) (a-b) to the 2nd power - 4a to the 2nd power b = (a-b + 2ab) (a-b-2ab).

The method of extracting common factors is one of the basic methods of factoring algebraic formulas, which is actually based on the multiplicative distributive law of elementary schools. That is, when all items of a polynomial contain the same factor, the same factor can be proposed outside the parentheses. For example:

x³+xx（x²+1）

Note: It is important to keep in mind that extracting common factors is a treatment of algebraic formulas, not equations!

Extracting the Common Factor Method:

4x^2-2x=0

The common factor 2x can be proposed

becomes 2x(2x-1)=0

The solution of the equation can be found as 0 or 1 2

If you have any questions, you can ask them.

a^2-4b^2+3a-6b

a-2b)(a+2b)+3(a-2b) square difference formula = (a-2b)(a+2b+3) extracts the common factor 4m2-4m+2n-n 2

4m 2-n 2-(4m-2n) grouping = (2m-n)(2m+b)-2(2m-n) squared difference formula = (2m-n)(2m+b-2) to extract the common factor.

6. Let A be a and B be B

then a=2b column equation a+40= b+40) substitute a into equation 2b+40=

Remove parentheses 2b+40=

The solution yields b=60 (kilograms).

a = 2b = 120 (kg).

It's about the same, let it be an unknown, and the equation will be easy to solve.

The solution is x=60 and 2x=120

The solution is x=4 3x=12

12 2 = 6 (kg) 15-6 = 9 (kg) 14-9 = 5 (kg).

Barrel A is 5 kg, and barrel B is 9 kg.

bar diameter plus 1 circumference.

9.It takes 6000 80 = 75 kg of seawater to dry 1 kg of salt, and 80 * 6000 = kg of salt can be dried per kilogram of seawater.

List the binary equations to solve, for example, in problem 6, let A have x, B has y, x 2y, x 40 1 6 (y 40), and solve x,y.