12)4x – 6y – 8 + 3z -11x – 7z + 5y – 2 + 16x=9x-y-10-4z
l)5a + 2a =7a
2)6b-4b=2b
15) 10a2+7ab-4a2+3b2-ab-6a2-4ab-5b2=2ab-2b2
24) 2z3n+2– 5z3+6z2-4z3n+2 +3z3-7z2 +5z3n+2– 9z3+15z2-8z3n+2=3z3n+2-11z3+14z2
16)8x3y2-5x2y3+2x2y3-6x3y 2=2x3y 2-3x2y3
3) 2x+7x-5x=4x
4)3y-y-4y + 8 y
5)4a-5b-2a-3b=2a-2b
6)7a2 – 6a – 5a2 + 3a
2.
44) {- 5xn-1-[-4xn + (-2x3 + 3xn – 4xn-1 ) ]- (xn – 6x3 – 3xn-1 ) } – [7x3 – (xn-1 – 2xn )]=(-5xn-1-(-4xn-2x3+3xn-4xn-1)-xn+6x3+3xn-1)-(7x3-xn-1+2xn)=(-5xn-1+4xn+2x3-3xn+4xn-1-xn+6x3-3xn-1)-7x3+xn-1-2xn=-5xn-1+4xn+2x3-3xn+4xn-1-xn+6x3-3xn-1-7x3+xn-1-2xn=x3-2xn-3xn-1
1) 5a – (2a + 3b)=5a-2a-3b=3a-3b
11) 4x2y-(3xy2 +5x2y) + 12xy2=4x2y-3xy2-5x2y+12xy2=9xy2-x2y
3)4y – (y – 3)=4y-y+3=3y+3
2)7a – (4a – 2y)=7a-4a+2y=3a+2y
4) 9m + (6n-7 m )=9m+6n-7m=2m+6n
5)(3a2 – 5a ) – ( a2 – 4a )=3a2-5a-a2+4a=2a2-a
6)5b + ( – 3b – 2c ) + (b + 4c)=5b-3b-2c+b+4c=3b+2c
7)(3k – 6n ) + (-2k + 6n)=3k-6n-2k+6n=k
8) (4x + 3) + ( 7 – 2x)=4x+3+7-2x=2x+10
9) (10x3 – 4x2) – ( 2x2 – 5x3)=10x3-4x2-2x2+5x3
3.
26) (xy+yz-xz)/xyz=(3/2*12/5+12/5*4/3-4/3*3/2)/(3/2*12/5*4/3)=(36/10+48/15-2)/(144/30)=(180/30+86/30-60/30)/(144/30)=(206/30)/(144/30)=206/30*30/144=206/144=103/72
x=1 1/2
y=2 2/5
z=1 1/3
1 ) 2a + 5b=-7
a = 4
b = -3
2) 4m – 3n + 10=14
m = – 5
n = -8
3) 5x + 2 y – 3 z + 7=12
x = 6
y = -17
z = -3
4) 2ab – 3bc – 4ac=-46
a = 4
b =-2
c = 3
5) 3 x -4 y + xy – 46=-16
x =-2
y = -6
6) 2ab -7 (a – 2b)=24-42+28=10
a = 6
b = 2
7 ) a(2b + 5 c ) – 4 b ( a – 3 c ) =60-30-60-240=-270
a = -3
b = 5
c = -4
8) 4(3 — m) + 2(n +1) — 3(5 — k)-11=12-28+8+2-15-24=-69
m = 7,
n = 4
k = 8
9) (4 -x )(2 y + l)-(3 y -2 )(4 x + 3)-35=4-6+24+3=25
x = 6
y = 0
4.
l)a3*a5=a8
2 ) b7*b2=b9
3)(-m2)* m=-m3
4) ( – x2) ( – x6)=x8
5) y5 ( -y6 )=-y11
6) c2 *c5 *c4=c11
7) pn * p2=pn+2
8) am * a4=am+4
9 ) xn *xk * -x3=xn+k+3
10) yn+2 * y3=yn+5
5.
1) (x + 2)5=5x+10
2) 6 (3y-4 )=18y-24
3) (2m + 3 n )7=14m+21n
4) c(2a + 5b)=2ac+5bc
5)-4 a ( 3 b – 2 a )=8a2-12ab
6) (-5x + 3y)2x=6xy-10x2
7) (3a – 4 b + 5c)(-2)=8b-6a-
8) x3(x2 + x – 2)=x5+x4-2x3
9) (3y2+ 4 y – 1) (- 5y6)=-15y8-20y+5y6
10) 4a3 (2a2 – 5 a -3 )=8a5-20a4-12a3
6.
21) (2x – 3)(9x2 + 12x + 5)=18x3+24x2+10x-27x2-36x-15
23) (x – y)(x3 + x2y + xy2 + y3)=x4+x3y+x2y2+xy3-x3y-x2y2-xy3-y4
25) (2y5 – y4– 3 y3+ 4 y2)(5 + y)=10y5-5y4-15y3+20y2+y6-y5-3y4+4y3
1 )(a + 2)(a -3 )=a2-3a+2a-6
4) ( 2 y – 5 ) ( 4 y – 3 )=8y2-6y-20y-15
7) (2 – 4a)(1 – 3a)=2-6a-4a+12a2
2) (5a + 1)(2a + 4)=10a2+20a+2a+4
5) (3a + 4)(2a – 3)=6a2-9a+8a-12
8) ( 3 – 2 a)(5a + 1)=15a+3-10a2+2a
3) (3b + 2 ) ( 4 – b )=12b-3b2+8-2b
7.
21) (3a4b5)3=27a12b15
22) (2x2y3)5=32x10y15
29 )[(x3)2]4=(x6)4=x24
34)- ( – x5)3]6=(x15)6=x90
1) ( a 3)2
2) (x2)4=x8]
3) ( -y4 ) 3 =-y12
4) (—x5)4=-x20
6) (x3)7=x21
7) ( – y 5)3=-y15
8.
1) 5b :b=5
2) 6a : (-6)=-a
3) (-3 x:) : ( – x)=3
4) 20z : 5z=4
5) 6mn : 3 n=2m
6) 8ab : 4b=2a
7) 15xy : (-3 x)=-5y
8) 9abc : 6bc=1,5a
9) 8xyz : (-2 xz)=-4y
10) (-12mn) : 4mn=3
9.
1) (m + n )2=m2+2mn+n2
2) (p -q)2=p2-2pq+q2
3) (c -d)2=c2-2cd+d2
4) (2 + a)2=4+4a+a2
5) (3 – b )2=9-6b+b2
6) (x + 5)2=x2+10x+25
7) (x + 1)2=x2+2x+1
8) (3a – b )2=9a2-6ab+b2
9) (5z + t)2=25z2+10zt+t2
10) (a – 4)2=a2-8a+16
14
1) (x + y )3=x3+x2y+xy2+y3
5) (3 – m )3=27-27m+3m3-m3
9) ( c – 3 d )3=c3-3c2d+9cd2-9d3
5) ( a – b )3=a3-a2b+ab2-b3
6) (x- 2 ) 3=x3-2x2+4x-8
10) (2x-3y)3=8x3-12x2y
3) (p + q)3=p3+p2q+pq2+q3
7 ) ( y – 3 )3=y3-3y2+9y-27
4) (2 + a)3=8+4a+2a2+a2
8) (a + 2b)3=a3+2a2b+4ab2+8b3
15
1) (a + 3x)3 = a3+ 3 a 2x + 9ax2+ 27x3
3) (1+ 2 a ) 3 = 1 + 2a+ 4a2+ 8a3
5) ( 2 x 3 + 3x ) 3 = 8x9+12x8 + 18x6+27x3
7) (15a3+ 4 a ) 3 = 3375+ 225a10+ 240a 5 + 64a3
9) (5+ 6a4)3= 125 + 150a4 + 180a8+216a12
2) (? -b)3 = ? – 3 z2b + ? – ?
4) (5x – 2)3 = 125x3– 50x2+ 20x- 8
6) (?-5a3)3 = ? -15 a3 b8 + ? -?
16) (12x5y3– 5x4y6)3 = 1748x15y9– 144x14y12+ 300x13y 15 – 125x12y 18
10) (?+ ?)3 = ?+6a2b+ 12ab2 + ?
24
1) a 2 + 2ab + b 2=(a+b)2
4) a 2 – 6 a + 9=(a-3)2
7) m2 +n 2 – 2mn=(m-n)2
10) 4a2+4a +1=(2a+1)2
2) a 2 – 2ab + b 2=(a-b)2
5) 2cd + d 2 + c 2=(d+c)2
8) x2 + 2x + 1=(x+1)2
3) a2 + 6a + 9=(a+3)2
6) – 2pq + p 2 + q 2=(p-q)2
9) x2– 2 x + 1=(x-1)
25
1) a3+3a2b + 3ab2 +b3=(a+b)3
3) m3+ 6m2a + 12ma2 + 8k3=(m+2k)3
5) 15m + 75m2 +1 + 125m3=(5m+1)3
2) x3 – 3x2y + 3xy2 – y3=(x-y)3
4) a3 – 6a2b + 12ab2 – 8b3=(a-2b)3
6) 64 + 48a2 – 96a – 8a3=(4-2a)3
7) a3+ 216 + 108a + 18a2 =(a+6)3
11) 64a6 – b3 + 12a2b2 – 48a4b=(64a6-b)3
10) 8 p3 + 54p + 36p2 + 27=(2p+3)3
9) 3 6 y – 8 – 5 4 y2 + 2 7 y3=(3y-2)3
26
1) p3 + q3=(p+q)(p2 +pq+q2)
2) p3 – q3=(p-q)(p2 -pq+q2)
3) a 3+8=(a+2)(a2+2a+4)
4) b 3 – 27 =(b-3)(b2-3b+9)
5)y3 + 1 =(y+1)(y2+y+1)
6) a3– 8=(a-2)(a2-2a+4)
7) p3 -1=(p-1)(p2-p+1)
8) m3+64=(m+4)(m2+4m+16)
9)1 – q 3=(1-q)(1-q+q2)
10) 1 + c3=(1+c)(1+c+c2)
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