Solution: The original formula =3X+2Y+4X+3Y=7X+5Y.
When x = 5 and y = 3.
Original formula =5*7+(-3)*5+20.
2.(5a 2-3b 2)+(a 2+b 2)-(5a 2+3b 2), where a =- 1 and b = 1.
=5a^2-3b^2+a^2+b^2-5a^2-3b^2
=a^2-5b^2
=(- 1)^2-5* 1^2
= 1-5
=-4
3.2 (A2B+AB 2)-2 (A2B-1)-2AB 2-2 where a =-2 and b = 2.
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0
1. It is known that A and B are two real roots of the equation x 2+2x-5 = 0.
Find the value of (a 2+2ab+2a) (b 2+2ab+2b).
Derived from the fact that A and B are two real numbers of the equation x 2+2x-5 = 0:
AB=-5，A+B=-2
A^2+2AB+2A)(B^2+2AB+2B)
=AB(A+2B+2)(B+2A+2)
=-5(-2+B+2)(-2+A+2)
=-5AB
=25
2, 1/2(x+y+z) squared+1/2 (x-y-z) (x-y+z)-z (x+y), where x-y=6 and xy=2 1. Be specific.
Simplify:
1/2(x+y+z) squared+1/2 (x-y-z) (x-y+z)-z (x+y) =1
1/2[(x+y) square +2z(x+y)+z square ]+ 1/2[(x-y) square -z square ]-z(x+y)=]
1/2(x+y) square+1/2(x-y) square =x square +y square.
From x-y=6, xy=2 1, x+y = (x-y)+2xy = 78.
3. Find the value of 2ab-2a 2-4b 2-7 from a 2-ab+2b 2 = 3.
2ab-2a^2-4b^2-7
=2(ab-a^2-2b^2)-7
=-2(a^2-ab+2b^2)-7
=(-2)*3-7
=-6-7=- 13
4. If A = 2x 2+3xy-2x-3, B =-x 2+xy+2, and the value of 3A+6B has nothing to do with X, find the value of y..
Solution:
3a+6b=6x^2+9xy-6x-9-6x^2+6xy+ 12
= 15xy-6x+3
=x( 15y-6)+3
5.9x+6x 2-3 (x-2/3x 2), where x=-2.
9x+6x -3(x-2/3x)
=9x+6x-3x+2x
=8x+6x
=8×(-2)+6×(-2)
=32- 12
=20
6.1/4 (-4x2+2x-8)-(1/2x-1), where x= 1/2.
1/4(-4x+2x-8)-( 1/2x- 1)
=-x+ 1/2x-2- 1/2x+ 1
=-x- 1
=-( 1/2)- 1
=- 1/4- 1
=-5/4
7.3x' y-[2x' y-(2xyz-x' z)-4x' z]-XYZ, where x =-2, y =-3, z = 1,
:3x ' y-[2x ' y-(2xyz-x ' z)-4x ' z]-XYZ
=3x'y-2x'y+2xyz-x'z+4x'z-xyz
=x'y-xyz+3x'z
=4*(-3)-2*3* 1+3*4* 1
=- 12-6+ 12
=-6
8.(5a 2-3b 2)+(a 2+b 2)-(5a 2+3b 2), where a =- 1 and b = 1.
=5a^2-3b^2+a^2+b^2-5a^2-3b^2
=a^2-5b^2
=(- 1)^2-5* 1^2
= 1-5
=-4
9,2 (A2B+AB 2)-2 (A2B-1)-2AB 2-2, where a =-2 and b = 2.
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0
10 squared, (x-21y-1) (x-21y+1)-(x-21y-1).
Where x = 1.7 and y = 3.9 (simplify first and then evaluate).
[(X-2 is 1Y)- 1][(X+2 is 1Y)+ 1]-(X-2 is1y-0/) square.
= (x+ 1Y) square-1-(x- 1Y) square +2 (x- 1Y)- 1.
= (x+ 1Y) square -(x- 1Y) square +2 (x- 1y) -(X-2
=2XY+2X-Y-2
=3.9*2.4+ 1.4
= 10.76
1. It is known that A and B are two real roots of the equation x 2+2x-5 = 0.
Find the value of (a 2+2ab+2a) (b 2+2ab+2b).
Derived from the fact that A and B are two real numbers of the equation x 2+2x-5 = 0:
AB=-5，A+B=-2
A^2+2AB+2A)(B^2+2AB+2B)
=AB(A+2B+2)(B+2A+2)
=-5(-2+B+2)(-2+A+2)
=-5AB
=25
2, 1/2(x+y+z) squared+1/2 (x-y-z) (x-y+z)-z (x+y), where x-y=6 and xy=2 1. Be specific.
Simplify:
1/2(x+y+z) squared+1/2 (x-y-z) (x-y+z)-z (x+y) =1
1/2[(x+y) square +2z(x+y)+z square ]+ 1/2[(x-y) square -z square ]-z(x+y)=]
1/2(x+y) square+1/2(x-y) square =x square +y square.
From x-y=6, xy=2 1, x+y = (x-y)+2xy = 78.
3. Find the value of 2ab-2a 2-4b 2-7 from a 2-ab+2b 2 = 3.
2ab-2a^2-4b^2-7
=2(ab-a^2-2b^2)-7
=-2(a^2-ab+2b^2)-7
=(-2)*3-7
=-6-7=- 13
4. If A = 2x 2+3xy-2x-3, B =-x 2+xy+2, and the value of 3A+6B has nothing to do with X, find the value of y..
Solution:
3a+6b=6x^2+9xy-6x-9-6x^2+6xy+ 12
= 15xy-6x+3
=x( 15y-6)+3
5.9x+6x 2-3 (x-2/3x 2), where x=-2.
9x+6x？ -3(x-2/3x？ )
=9x+6x？ -3x+2x？
=8x？ +6 times
=8×(-2)? +6×(-2)
=32- 12
=20
6.1/4 (-4x2+2x-8)-(1/2x-1), where x= 1/2.
1/4(-4x？ +2x-8)-( 1/2x- 1)
=-x？ + 1/2x-2- 1/2x+ 1
=-x？ - 1
=-( 1/2)? - 1
=- 1/4- 1
=-5/4
7.3x' y-[2x' y-(2xyz-x' z)-4x' z]-XYZ, where x =-2, y =-3, z = 1,
:3x ' y-[2x ' y-(2xyz-x ' z)-4x ' z]-XYZ
=3x'y-2x'y+2xyz-x'z+4x'z-xyz
=x'y-xyz+3x'z
=4*(-3)-2*3* 1+3*4* 1
=- 12-6+ 12
=-6
8.(5a 2-3b 2)+(a 2+b 2)-(5a 2+3b 2), where a =- 1 and b = 1.
=5a^2-3b^2+a^2+b^2-5a^2-3b^2
=a^2-5b^2
=(- 1)^2-5* 1^2
= 1-5
=-4
9,2 (A2B+AB 2)-2 (A2B-1)-2AB 2-2, where a =-2 and b = 2.
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0
10 squared, (x-21y-1) (x-21y+1)-(x-21y-1).
Where x = 1.7 and y = 3.9 (simplify first and then evaluate).
[(X-2 is 1Y)- 1][(X+2 is 1Y)+ 1]-(X-2 is1y-0/) square.
= (x+ 1Y) square-1-(x- 1Y) square +2 (x- 1Y)- 1.
= (x+ 1Y) square -(x- 1Y) square +2 (x- 1y) -(X-2
=2XY+2X-Y-2
=3.9*2.4+ 1.4
= 10.76
11.(3x+2y)+(4x+3y) where X=5, Y+3.
Solution: The original formula =3X+2Y+4X+3Y=7X+5Y.
When x = 5 and y = 3.
Original formula =5*7+(-3)*5+20.
12. (5a2-3b2)+(a2+b2)-(5a2+3b2), where a =- 1 and b = 1.
=5a^2-3b^2+a^2+b^2-5a^2-3b^2
=a^2-5b^2
=(- 1)^2-5* 1^2
= 1-5
=-4
13.2 (a2b+ab2)-2 (a2b-1)-2ab2-2, where a =-2 and b = 2.
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0
14.2 a-(3a-2 b+2)+(3a-4 b- 1)=)，a=b= 1
=2a-3a+2b-2+3a-4b- 1
=(2-3+3)a+(2-4)b+(-2- 1)
=2a-2b-3=-3
15.5-( 1-x)- 1-(x- 1)，x= 1 1
=5- 1+x- 1-x+ 1
=4
③2x-(x+3y)-(-x-y)-(x-y)=()
=2x-x+3y+x+y-x+y
=x+5y
a=2，b=4
Found 2(a-b-54)+3(a+b)
=5a+b- 108
=5*2+4- 108
=-94
a=b= 1
Found a+b-2(a-b+ 1)
=-a+3b-2
=- 1+3-2
=0
26.-(2 x2-y2)-[2 y2-(x2+2xy)]= _ _ _ _ _ _。
27. If -3a3b2 and 5ax- 1by+2 are similar terms, then x = _ _ _ _ _, and y = _ _ _ _ _.
28.(-y+6+3 y4-y3)-(2 y2-3 y3+y4-7)= _ _ _ _ _ _。
29. The result of simplifying the algebraic expression 4x2-[7x2-5x-3( 1-2x+x2)] is _ _ _ _.
30.2 a-B2+c-D3 = 2a+()-D3 = 2a-D3-()= c-()。
3 1.3a-(2a-3b)+3(a-2b)-b = _ _ _ _ _ _。
32. The simplified algebraic expression x-[y-2x-(x+y)] is equal to _ _ _ _.
33.[5a 2+()a-7]+[()a2-4a+()]= a2+2a+ 1。
34.3x-[y-(2x+y)]=______。
35.Simplify | 1-x+y |-x-y | (where x < 0, y > 0) equals _ _ _ _.
36. It is known that x≤y, x+y-| x+y-| x-y | = _ _ _ _ _
37. Given x < 0 and y < 0, simplify | x+y |-| 5-x-y | = _ _ _.
38.4a2n-an-(3an-2a2n)=______。
39. If you add -3x2y+2x2-3xy-4 to a polynomial, you get.
2x2y+3xy2-x2+2xy，
Then this polynomial is _ _ _ _.
40.-5xm-xm-(-7xm)+(-3xm)=______。
4 1. When a=- 1 and b=-2,
[a-(b-c)]-[-b-(-c-a)]=______。
43. When a=- 1, b= 1 and c=- 1,
-[b-2(-5a)]-(-3b+5c)=______。
44.-2(3x+z)-(-6x)+(-5y+3z)=______。
45.-5an-an+ 1-(-7an+ 1)+(-3an)= _ _ _ _ _ _。
46.3 a-(2a-4 b-6c)+3(-2c+2b)= _ _ _ _ _ _。
48.9 a2+[7 a2-2a-(-a2+3a)]= _ _ _ _ _ _。
50. When 2y-x=5, 5 (x-2y) 2-3 (-x+2y)-100 = _ _ _.