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(6x+8)(3x^2+2x+8)
6x(3x^2+2x+8) +8(3x^2+2x+8)
6x *3x^2 +6x*2x+6x*+8 +8*3x^2+8*2x+8*8
18x^3+12x^2+48x+24x^2+16x+64
18x^3 +(12+24)x^2+16x+64
18x^3+36x^2 +16x+24

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Given
V=1100 cu.in
h= 8in
b = 10in
l=?
v=l*b*h
1100 =l*8*10
1100 =80l
1100/80=l
13.75 =l
length of the box is 13.75 in

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4(x+7)=-9(x-6)
4*x +4*7 =-9*x -9*(-6)
4x+28 =-9x+54
4x+9x=54-28
13x=26
13x /13 =26/13
x =2

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let width =x
length =x+65
given perimeter =310
perimeter =2(l+w)
310=2(x+65+x)
310=2(2x+65)
310=4x+130
310-130=4x
180=4x
x=180/4
x=45
therefore;
width =45
and length =x+65
=45+65
=110

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5[3-3(x-1)]+1=2(-64-x)+2x+64
solution:
5[3-3x-3]+1= -128-2x+2x+64
5(-3x)+1=-128+64
-15x+1= -64
-15x=-64-1
-15x=-65
x=-65/-15
x=13/3

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A number increased by 5 is equal to 34.
let the number be x
so,
the number increased by 5 means =>x+5
the equation becomes
x+5=34
x=34-5
x=29

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4a-2b+3a+b-5a
take the like terms together
4a+3a-5a-2b+b
7a-5a-2b+b
2a-b

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3x+5y+4z if x=12,y=8 and z=6
solution:
substitute the values of x,y,z in the given equation
3x+5y+4z
=3*12+5*8+4*6
=36+40+24
=100

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18x^2 =3*3*2 *x^2
27x^4 =3*3*3*x^2 *x^2
30x^3 =3*5*2*x^2*x
GCF =3*x^2
=3x^2

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let the length of the rectangle =x
width =x-3
given ,
perimeter =62ft
2(l+w) =62ft
2(x+x-3) =62ft
2(2x-3)=62ft
4x-6 =62ft
4x=62+6 =68ft
x=68/4
x=17ft
therefore
length =17 ft
and
width =17-3
=14ft

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length of finger nail in m month =10+3m
length of finger nail in 8 months =10+3*8
=10+24 =34mm
length of finger nail in 3 years
3 years =3*12months
=36 months
length of finger nail in 36 month =10+3*36
=10+108 = 118mm

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1/2(6-z)=z
solution:
1/2(6-z) *2= 2*z
(6-z)=2z
6=2z+z
6=3z
6/3=z
z=2

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slope point form is
(y-y1)=m(x-x1)
m =0, x1=4 and y1 =-2
[y-(-2)] =0[x-4]
y+2 =0
the slope intercept form is
y=mx+b
ie,
y+2 =0
y=-2

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nickels =N
dimes =D
total number of coins =18
N+D=18
N=18-D -----------(1)
total nickels and dime is 1.45
5N+10D = 145 --------------(2)
substitue the value of N in(2)
5(18-D)+10D= 145
5*18 -5D +10D =145
90 +5D=145
5D=145-90
5D=55
D=11
N+D=18
N+11+18
N=7
there are 7 nickels and 11 dimes
Proof:
5N+10D=145
5*7 +10*11=145
35+110=145
145=145

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let width =x
length =2x
perimeter =210m
perimeter =2(l+w)
2(l+w) =210m
2(2x+x)=210
2(3x) =210
6x=210
x=210/6
x=35
ie,
width = 35m
length =2*35 =70m

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(5.9x^3+3.4x^2-7)-(2.9x^3-9.6x^2+3)
=(45x^3 +12x^2 -7) -(18x^3-54x^2+3)
remove the paranthesis
=45x^3+12x^2 -7 -18x^3 +54x^2 -3
take the like terms together and simplify
45x^3-18x^3 +12x^2+54x^2 -7-3
=> (45-18)x^3 + (12+54)x^2 -(7+3)
=> 27x^3 + 66x^2 -10

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There are 144 square inches in a square foot
Therefore, square feet X 144 = square inchs
given area of triangle =2.25 square feet
ie,
2.25 *144 squarefeet = 324 square inches
2.25sq ft =324 sqin

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cost of shirt =x
cost of jeans =x+10
total cost =$32
x+x+10 =32
2x+10 =32
2x=32-10
2x=22
x=11
cost of shirt =$11
cost of jeans =x+10
=$11+$10
=$21

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Grade for first eaxm =65%
grade for second exam = 85%
grade for third exam =77%
overall grade =20%
grade for final exam =x
overall grade = 40%
total grade =80%
(65% +85% 77%)20% +x*40% =80%
227% *20% +x*40%=80%
45.4% +40x% =80%
40x% =80%-45.4%
40x% = 34.6%
x% = 34.6%/40%
x%= 0.865
x=86.5%
grade score for final exam =86.5%

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1/8-3/4x=1/16
solution:
1/8 -3/4x = 1/16
-3/4x =1/16-1/8
-3/4x =1/16-1*2/8*2
-3/4x=1-2/16
-3/4x=-1/16
-3/4x *-4/3 = -1/16*(-4/3)
x=4/(16*3)
x=1/4*3
x=1/12

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2x^2+30x+52
solution:
2(x^2 +15x +26)
=> 2(x^2+13x+2x+26)
=>2[x(x+13)+2(x+13)]
=>2(x+13)(x+2)

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8m(3rd power) + 64
=> 8m^3+64
8m^3 =(2m)^3
64=4^3
8m^3+64
=(2m)^3 +4^3

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y^2-49
It is in the form
a^2-b^2 =(a-b)(a+b)
y^2-49 =y^2-7^2
=(y-7)(y+7)
y=+7,or y=-7
y=7,-7

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A group of dogs and ducks have a total of 99 heads and legs among them. There are twice as many ducks as there are dogs. How many are there of each animal
solution:
let Dogs =X
Duck =Y
Dogs having 4 legs and 1 head
=>4X+1X=5x
duck is having 2 legs and 1 head
=>2Y+1Y=3Y
given total legs and heads =99
5X+3Y=99--------------(1)
also given
ducks =2 dogs
Y=2x----------(2)
substitute the value of Y in (1)
5X+3Y=99
5X+3(2X)=99
5x+6x=99
11X=99
X=99/11
x=9
y = 2X
Y=2*9
Y=18
there are 9 dogs and 18 ducks

Proof:
x=9,y=18
5x+3y=99
5*9+3*18=99
45+54=99
99=99
RHS=LHS

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let the numbers be x and y
sum of numbers is 185
x+y =185-----------(1)
differnce is 57
x-y =57------------- (2)
(1) +(2) =
x+y=185
x-y=57
=> 2x= 242
x=242/2
x=121
x-y=57
121 -y=57
-y=57-121
-y= -64
y=64
therfore the two numbers are
121 and 64

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total length of the wooden rod =72in
length of first rod =x in
length of second rod =(x+6)in
x+(x+6) =72
2x+6 =72
2x=72-6
2x= 66
x=33
x+6 =39
length of the rods are 33in and 39 in

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60% of x =18
60% *x =18
60/100 *x=18
60x=18*100
x=18*100/60
x=30
30 is the number

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total number of stamp = x
stamps from Canada =1/2x
stamps from france =1/4x
stamps from mexico =1/8x
stamps from italy =1/16x
stamps from US=4
ie,
1/2x+1/4x+1/8x+1/16x+4 =x
(1/2+1/4+1/8+1/16)x +4=x
15/16x+4=x
15x/16 -x =-4
15x-16x/16 =-4
-x/16 =-4
x=(-4)*(-16)
x=64
total number of stamps =64

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4(8-6)^2 + 4*3-2*8/4
=
4(2)^2+12-2*2
= 4*4+12-4
=16+12-4
=28-4
=24

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20y^3+5y^2-15y
solution :
20y^3 +5y^2-15y
here 5y is common
so the equation becomes
5y(4y^2+y-3)
now you have to factor
4y^2+y-3 =4y^2+4y-3y-3
4y(y+1)-3(y+1)
(4y-3)(y+1)
20y^3 +5y^2-15y =5y(4y-3)(y+1)

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4x-6+2x-5
solution:
take the like terms together and simplify
4x-6+2x-5
=4x+2x-6-5
=6x-11