(a-2b + 3C) (- a-2b-3c) = () square - () square

(a-2b + 3C) (- a-2b-3c) = () square - () square

The original formula = (- 2b) &# 178; - (a + 3C) &# 178;
Square of (a + 3b) square of (2b)
Several factorization problems
^How many power
x^4+x^3+x^2-1
x^4-3x^2+1
x^4-7x^ ×2y^2+81y^4
x^8+x^4+1
2(x^2-3ab)+x(4a-3b)
X ^ 4-7x ^ × 2Y ^ 2 + 81y ^ 4 × is a multiplication sign
X ^ 4 + x ^ 3 + x ^ 2-1 = x ^ 3 (x + 1) + (x + 1) (x-1) = (x + 1) (x ^ 3 + x-1) x ^ 4-3x ^ 2 + 1 = x ^ 4-2x ^ 2 + 1-x ^ 2 = (x ^ 2-1) ^ 2-x ^ 2 = (x ^ 2 + x-1) (x ^ 2-x-1) x ^ 4-7x ^ × 2Y ^ 2 + 81y ^ please confirm the title x ^ 8 + x ^ 4 + 1 = x ^ 8 + 2x ^ 4 + 1-x ^ 4 = (x ^ 4 + 1) ^ 2-x ^ 4 = (x ^ 4 + x ^ 2 +
x^4+x^3+x^2-1
=x^3*(x+1)+(x+1)*(x-1)=(x+1)*(x^3+x-1);
x^4-3x^2+1
=（x^2-(3+sqrt(5))/2）*（x^2-(3-sqrt(5))/2）
=(x-sqrt ((3 + sqrt (5)) / 2)) * (x + sqrt ((3 + sqrt (5)) / 2)) * (x-sqrt ((3-sqrt (5)) / 2)) * (x + sq... Expansion)
x^4+x^3+x^2-1
=x^3*(x+1)+(x+1)*(x-1)=(x+1)*(x^3+x-1);
x^4-3x^2+1
=（x^2-(3+sqrt(5))/2）*（x^2-(3-sqrt(5))/2）
=(x-sqrt((3+sqrt(5))/2))*(x+sqrt((3+sqrt(5))/2))*(x-sqrt((3-sqrt(5))/2))*(x+sqrt((3-sqrt(5))/2));
X ^ 4-7x ^ × 2Y ^ 2 + 81y ^ 4 =? What topic?
X ^ 8 + x ^ 4 + 1 = no real solution
The solution of imaginary number is = (x + (- 1 + sqrt (3) I) / 2) ^ (1 / 4)) * (x + (- 1-sqrt (3) I) / 2) ^ (1 / 4));
2 (x ^ 2-3ab) + X (4a-3b) = 2 * x ^ 2 + (2a-3b / 2) x-3ab = (x-2a) (x + 3B / 2)
First simplify and then evaluate: 2 (the square of a, B + the square of AB) - 2 (the square of a, B-1) - the square of 2ab-2
2 (the square of a, B + the square of AB) - 2 (the square of a, B-1) - the square of 2ab-2
=2a²b+2ab²-2a²b+2-2ab²-2
=0
Fifty-five
The original formula = 2A & # 178; B + 2Ab & # 178; - 2A & # 178; B + 1-2ab & # 178; - 2 = - 1
Expand and simplify the brackets to 0
Equal to 0
Several factorization questions to ask for help!
x^4+4x^3-12x-9
x^3-y^3-x^2-xy-y^2
a^8+a^4b^4+b^8
(a^2-1)(b^2-1)-4ab
Please give the process and ideas
X ^ 4 + 4x & sup3; - 12x-9, replace X & sup2
=x^4+4x³+3x²-3x²-12x-9
=x²(x²+4x+3)-3(x²+4x+3)
=(x²+4x+3)(x²-3)
=(x+1)(x+3)(x²-3)
=(x+1)(x+3)(x+√3)(x-√3)
X & sup3; - Y & sup3; - X & sup2; - xy-y & sup2;, complement X & sup2; y term and XY & sup2; term
=x³+x²y+xy²-x²y-xy²-y³-x²-xy-y²
=x(x²+xy+y²)-y(x²+xy+y²)-(x²+xy+y²)
=(x-y-1)(x²+xy+y²)
A ^ 8 + (a ^ 4) (b ^ 4) + B ^ 8, remember a & sup2; + B & sup2; = (a + b) & sup2; - 2Ab
=a^8+2(a^4)(b^4)+b^8-(a^4)(b^4)
=(a^4+b^4)²-(a²b²)²
=(a^4+b^4+a²b²)(a^4+b^4-a²b²)
=(a^4+2a²b²+b^4-a²b²)(a^4-a²b²+b^4)
=[(a²+b²)²-(ab)²](a^4-a²b²+b^4)
=(a²+b²-ab)(a²+b²+ab)(a^4-a²b²+b^4)
(A & sup2; - 1) (B & sup2; - 1) - 4AB
=a²b²-a²-b²-4a²+1
=a²b²-4ab-a²-b²+1
=a²b²-2ab+1-a²-2ab-b²
=a²b²-2ab+1-(a²+2ab+b²)
=(ab-1)²-(a+b)²
=[(ab-1)-(a+b)][(ab-1)+(a+b)]
=(ab-1-a-b)(ab-1+a+b)
First, simplify, then evaluate. (1) the square of 2Ab - the square of 3A B-2 (the square of a, the square of b-ab), where a = - 1, B = - 2
The square of 2Ab - the square of 3A B-2 (the square of a, the square of b-ab), where a = - 1, B = - 2
=2ab²-3a²b-2a²b+2ab²
=4ab²-5a²b
=4*(-1)*(-2)²-8(-1)²*(-2)
=-16+16
=0
The square of 2Ab - the square of 3a, B-2 (the square of a, the square of b-ab), and,
=The square of 2Ab - the square of 3A the square of b-2a + the square of 2Ab
=ab(4b-5a)
=2*(-8+5)
=-6
Several factorization problems
1. The fourth power of X + the second power of X + 1
2. Given A-B = 1 / 2, ab = 1 / 8, find the value of - 2A ^ 2B ^ 2 + AB ^ 3 + A ^ 2B
3.(a+b)^2-6(a+b)+9
4. Given that x is a rational number, then the value of polynomial X-1-1 / 4x ^ 2 ()
A. It must be negative B. It can't be positive
C. It must be positive D. it may be positive or negative or zero
5. Factoring in real numbers
（1）5x^2-3
(2)a^4-9
6. If a + B = m, ab = n, then a / B + B / A=______ ,[1/(a+1)]+[1/(b+1)]=_________
7. If three sides a, B, C of a triangle satisfy a ^ 2 + 2B ^ 2 + C ^ 2-2ab-2bc = 0, try to explain the shape of the triangle
8. Given a ^ 2 + B ^ 2 = 5, C ^ 2 + D ^ 2 = 2, find the value of (AC + BD) ^ 2 + (AD BC) ^ 2
9. Given (a ^ 2 + B ^ 2-4) (a ^ 2 + B ^ 2) + 4 = 0, find a ^ 2 + B ^ 2
10.-10x^2y-5xy^2+15xy
11.(x^2+1)^2-2x(x^2+1)
12.1-x^2-y^2+2xy
13. Known: a + B = 1 / 2, ab = 3 / 8, find the value of a ^ 3B + 2A ^ 2B ^ 2 + AB ^ 3
x^4+x^2+1
== x^4 + 2 * x^2 + 1 - x^2
== （x^2 + 1）^2 - x^2
== （x^2 + x + 1） * （x^2 - x + 1）
3.(a+b-3)^2
Five
(2)(a^2+3)(a^2-3)
First simplify, then evaluate the square of a + AB / b △ the square of a - the square of B / AB + the square of B-A / a - the square of 2Ab + B [where a = 3, B = 1 / 2]
The square of a + AB / b ／ the square of a - the square of B / AB + the square of B-A / a - the square of B + B = a (a + b) / b ／ (a + b) (a-b) / AB - (a-b) / (a-b) &# 178; = A & # 178; / (a-b) - 1 / (a-b) = (A & # 178; - 1) / (a-b) = (3 & # 178; - 1) / (3-1 / 2) = 8 / (5 / 2) = 16 / 5
On factorization
1. What is x (- A & sup2;) & sup3; X (- A & sup3;) & sup2; = to the fifth power of - a?
2. If (X-2) & sup2; + (y + 3) & sup2; = 0, then (x + y) & sup2; = what?
3. The following calculation is correct: a.2a + 3B = 5ab B. (- AB) & sup2; = A & sup2; B & sup2;
4. No matter what rational numbers m and N are, the value of M & sup2; + n & sup2; - 2m-4n + 8 is always a negative number, b 0 C positive number and D non negative number
5. X (X-Y) & sup2; - Y (Y-X) & sup2; can be reduced to a, (X-Y) & sup2; B, (X-Y) & sup3; C, (Y-X) & sup2; D, (Y-X) & sup3;
6. Calculation
(the process should have) 1. [(XY & sup2;) & sup2;] & sup3; + [(- XY & sup2;) & sup2;] & sup3;
2.（-1/2a²b）（2/3b²-1/3a+1/4)
3. Factorization 25 (a + b) & sup2; - 16 (a-b) & sup2;
1.-a^5X(-a^6)Xa^6=a^17
2. If (X-2) & sup2; + (y + 3) & sup2; = 0, then (x + y) & sup2; = what?
It is concluded that x = 2, y = - 3, (x + y) & sup2; = (2-3) ^ 2 = 1
3. B. (- AB) & sup2; = A & sup2; B & sup2; correct
4 M & sup2; + n & sup2; - 2m-4n + 8 = (m-1) ^ 2 + (n-2) ^ 2 + 3 is always positive
5x(x-y)²-y(y-x)²=x(x-y)²-y(x-y)²=(x-y)(x-y)²=(x-y)^3
6 1.[（xy²）²]³+[（-xy²）²]³=[（x^2y^4]³+[（x^2y^4]³=x^6y^12+x^6y^12=2x^6y^12
2.（-1/2a²b）（2/3b²-1/3a+1/4)
=-1/2a²bX2/3b²-(-1/2a²bX1/3a)+(-1/2a²bX1/4)
=-1/3a²b^3+1/6a^3b-1/8a²b
3. Factorization 25 (a + b) & sup2; - 16 (a-b) & sup2; square difference formula
=[5(a+b)+4(a-b)][5(a+b)-4(a-b)]
= [5a+5b+4a-4b][5a+5b-4a+4b]
=(9a+b)(a+9b)
First simplify and then evaluate, (2a's Square, b-ab's square + 1 / 2Ab) / (- 1 / 2Ab), where a = - 1, B = 2
(the square of 2a, the square of b-ab + 1 / 2Ab) / (- 1 / 2Ab)
=-2(2a^2b-ab^2+ab/2)/(ab)
=-2(2a-b+1/2)
=-4a+2b-1
When a = - 1, B = 2
The original formula = - 4 * (- 1) + 2 * 2-1 = 7
Calculation: 121 × 0.13 + 12.1 × 0.9-12 × 1.21=______ .
121×0.13+12.1×0.9-12×1.21=12.1×1.3+12.1×0.9-12.1×1.2=12.1×（1.3+0.9-1.2）=12.1×1=12.1．