A few math problems about factoring

1.(x+2)(x-2)

2.=a squared (x-y) - b squared (x-y) = (a squared - b squared) (x-y) = (x-y) (a+b) (a-b).

3.Extract the common factor ac to get the remainder of the perfect square = ac(a-2b) squared4d 2 3 or —2 3

5.Cross multiplication = (a-3)(3a+2).

6.Perfect square = (x-2y) squared and then squared (x-2y+1) (x-2y-1).

1.Decomposition factor: x squared - 4=

x-4)(x+4)__

2.Decomposition factor: the square of a (x-y) + the square of b (y-x) x-y) (a-b) (a+b).

3.Decomposition factor: the cube of a c-the square of 4a bc + the square of 4ab c?I didn't understand what it meant.

4.If the square of the polynomial x + kx + 1 9 is a perfect square, then the value of k is

a.—3 b 3 c 1 3 or —1 3 d 2 3 or —2 3d53a squared -7a-6=

3a+2)(a-3)

The square of +4y-4xy-1

x-2y+1)(x-2y-1)

1 original = (x+2)(x-2).

2/=a^2(x-y)-b^2(x-y)=(a+b)(a-b)(x-y)

3 =ac(a2-4ab+4b 2)=ac(a-2b) 24 d5 with cross multiplication.

3a +2a -3

Original = (3a+2)(a-3).

6/=(x-2y)^2-1=(x-2y-1)(x-2y+1)

of the squared - 2006-2007 (easy calculation).

Factoring) (x+y) [a+(a-b)].

x+y)(2a-b)

(easy to calculate).

4.The circumference of the rectangle is 28 cm, and the length of the two sides is x,y, if the cubic of x + the square of x y-the square of xy - the cubic of y = 0, find the area of the rectangle (there is a process).

2x+2y=28 x+y=14

x to the third power + x to the square y - xy to the square - y to the third power = 0x 2 (x + y) - y 2 (x + y) = 0

x+y)(x+y)(x-y)=0

x+y)^2](x-y)=0

then x=y=(x+y) 2=7

The area of the rectangle is s=xy=49 (square centimeters).

5.Factoring the cubic of -6(x-y) to the cubic of -3y(y-x) results in ().

The cubic of 6(x-y) and the cubic of -3y(y-x) = -6(x-y) 3+3y(x-y) 3

x-y)^3(3y-6)

3(x-y)^3(y-2)

of the square +36-12 2006

Perfectly squared formula, hehe

1.Solution: Original formula = 2007 (2007-2006) = 2007 * 1 = 2007

2.Solution: Original formula = (a+a-b)(x+y).

2a-b)(x+y)

3.Solution: Original formula = 99*(100-1).

99*100-99=9000-99=98014.Solution: x 3-y 3=-x 2*y+xy 2(x-y)(x 2+xy+y 2)=-xy(x-y)x 2+xy+y 2=-xy

x+y)^2=0

If x+y=0, then there must be a number that is not positive, so it is discarded.

x-y=0 i.e. x=y

2(x+y)=28,∴x=y=7

Area=7*7=49

5.Solution: Original formula =-6(x-y) 3+3y(x-y) 3=(x-y) 3· (-6+3y)

3(x-y)^3(y+2)

Untie; 1；2007 (2007-2006) equals 2007 2;(x y)(a a b) is equal to bx by 3; The square of (100 1) is finally equal to 9801 4 and the square of (x y) (x y) obtained by factoring the original equation 0 gives x y 0 to get x y 2x 2y 28 x y 7, i.e. 7 7 49 5 of the area(6 3y)(y x) to the third power 6;4000000

1. Use factorization to calculate.

This problem is found using the formula of perfect square difference).

2) 2. Simple calculation by factorization.

3. Decomposition factor: a -a+1 a=

4. Fill in the blanks: x + (8x) + 16 = (x + (4)) =

9x²+2x+1/9=(3x+(1/3))²

5. Calculate by factorization:

=x^3+x^2+5x^2+11x+6

x^2(x+1)+(5x+6)(x+1)

x^2+5x+6)(x+1)

x+1)(x+2)(x+3)

It is not possible to solve the original formula =(x +ax+2)(x +bx+4) or =(x +ax-2)(x +bx-4).

x^4+(a+b)x^3+(6+ab)x^2+(4a+2b)x+8

or = x 4 + (a + b) x 3 + (-6 + ab) x 2 - (4a + 2b) x + 8

a+b=2 6+ab=-9 4a+2b=0

or a+b=2 -6+ab=-9 -(4a+2b)=0

There is no solution to both sets of equations.

You can't decompose a factor.

3.(y+1)^4+(y+3)^4-272

Let x=y+2

Original = (x-1)4+(x+1)4-272

2(x4+6x2+1)-272

2(x4+6x2-135)

2(x2-9)(x2+15)

2(x+3)(x-3)(x2+15)

2(y+5)(y-1)(y2+4y+19)

4.(xy-1)^2+(x+y-2)(x+y-2xy)

x+y)²-2(1+xy)(x+y)+4xy+1-2xy+x²y²

x+y)²-2(1+xy)(x+y)+(1+xy)²

x+y)²-1+xy)(x+y)-(1+xy)(x+y)+(1+xy)²

x+y)(x+y-1-xy)-(1+xy)(x+y-1-xy)

x+y-1-xy)(x+y-1-xy)

x+y-1-xy)²

Let the original formula =(x +ax+1)(x +bx+7) or =(x +ax-1)(x +bx-7).

x⁴+(a+b)x³+(ab+8)x²+(7a+b)x+7=x⁴-2x³-27x²-44x+7

or x + (a + b) x + (ab-8) x - (7a + b) x + 7 = x -2x -27x -44x+7

Comparing the coefficients on both sides of the equation yields.

a+b=-2

ab+8=-27

7a+b=-44

or a+b=-2

ab-8=-27

7a-b=-44

Solving these two systems of equations yields:

a=-7 b=5 [the second system of equations is unsolved].

So the original formula = (x -7x+1)(x +5x+7).

The first way: the original formula = ab (a + 2 ab + b) = 2 (2 3 + 2 2).

The second way: the original formula = n(n2-4)(n2-1), no matter when n takes any integer greater than 2, there is a factor of 120, so it is divisible by 120.

The third way: proof: (a3+b3)+c(a2+b2-ab)=(a+b)(a2+b2-ab)+c(a2+b2-ab)=(a2+b2-ab)(a+b+c) Because a+b+c=0, the proof is true.

The first way: =[4(x-1)+(x+2)]*4(x-1)-(x+2)]=3(5x-2)(x-2); The second way: =-2a square (x-4) square; The third way: =a(a-2)+(1+b)(1-b).

Results solved with Mathematica.

Question 1: 3 (-2 + x) (2 + 5 x) Question 2: -2 A 2 (-4 + x) 2 Question 3: (-1 + A - b) (1 + A + B).

The first pass - (x+2) +16 (x-1).

4(x-1)]^2-(x+2)^2

4x-4+x+2)(4x-4-x-2)=(5x-2)(3x-6)

3(x-2)(5x-2)

The second pass is -2a x +16a x-32a

2a^2(x^2-8x+4^2)

2(x-4)^2

The third lane a -2a + 1-b

a-1)^2-b^2

a+b-1)(a-b-1)

1、（a+3) (a-7)+25

a square - 4a - 21 + 25

a square - 4a + 4

a-2) squared.

x^6 - 3x^2

3x^2(x^4-1)

3x^2(x^2+1)(x^2-1)

3x^2(x^2+1)(x+1)(x-1)

x-2y)^2-4(2y-x)^2

5(x-2y)-2(2y-x)][5(x-2y)+2(2y-x)]

7x-14y)(3x-6y)

21(x-2y)(x-2y)

21(x-2y)^2

4、x^4-18x^2+81

x^2-9)^2

x-3)^2(x+3)^2

5. Knowing that 2x-y=1 3, xy=2, find 2x 4y 3 - x 3y 4

2x^4y^3 - x^3y^4

x^3y^3(2x-y)

xy)^3(2x-y)

6. If x and y are opposite to each other, and (x+2) 2-(y+1) 2=4, find the values of x and y.

x and y are inverse numbers to each other.

then y=-x, then (x+2) 2-(y+1) 2=4

is (x+2) 2-(-x+1) 2=4

x^2+4x+4-(x^2-2x+1)=4

6x=1x=1/6

Then y=-1 6

7. Knowing a+b=2, find the value of (a 2-b 2) 2-8 (a 2 + b 2).

a^2-b^2)^2-8(a^2+b^2)

a+b)^2(a-b)^2-8(a^2+b^2)

4(a-b)^2-8(a^2+b^2)

4(a^2-2ab+b^2)-8(a^2+b^2)

4a^2-8ab+4b^2-8a^2-8b^2

4(a^2+2ab+b^2)

4(a+b)^2

8. (a-2)(a 2+a+1)+(a 2-1)(2-a), where a=18

a-2)(a^2+a+1)+(a^2-1)(2-a)

a-2)[(a^2+a+1)-(a^2-1)]

a(a-2)

a=18a(a-2)

9. Simplification and evaluation: (a+b)(a-b)+(a+b) 2-a(2a+b), where a=1 3, b=-1 1 2

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

a+b)[(a-b)+(a+b)]-a(2a+b)

2a(a+b)-a(2a+b)

a(2a+2b-2a+b)

3aba=1/3,b=-1/1/2

3ab=3*(1/3)*(1/1/2)

20x n9 4-6 4+3 4=3 4(3 4-2 4+1)=3 4 multiplied by 66, the travel code is divisible by 11.

a-b)(x-y+z）

x^n(x-1)^2(x-1)