How do i factorise the below?

How do i factorise the below? (a+2)(2a)+7a+14 and 64x^2+80xy+25y^2

First one:


second:

The sides of an equilatersl triangle are 3x-1, 5y, and x+13. Find the measures of each side.

equilateral => 3x-1=x+13 => x=7

and x+7 turns into 7+13=20
and so all sides are 20 units

:)

simplify: -3(-2 - 6 x 2) - [4(2 - 4) - 2]

(5x-7)/5=(6x+4)/2

Since this is a proportion, we'll cross multiply the solve for x:

:)

(x-a)/(x+a) - (x+a)/(x-a)=7/12 solve the equation

then...









so x=a/7 or x=-7a but in either case
 and 

In Triangle ABC, Angle B = 15 degrees less than twice angle A and Angle C is more than angle A. Find angle C.

B=2A-15

C>A
and A+B+C=180
which becomes...
A+(2A-15)+C=180
C=180+15-3A
C=165-3A

so

Which sets our boundary to test for valid triangles. After trial and error (there's probably a better way) we can deduce the following.
The least value for C under these conditions is C=42 and the greatest is a little more than 142
so...these are pretty good approximations

 

the smallest number greater than 200 that is divisible by both 3 and 9

It is well known that if the digits of a number add to a multiple of 3 then so does the number (the same property holds for 9). We look for a number such that

2_ _ is a minimum, and divides 9

so we can see the least number possible must be 207

:)

Polynomial Multiplication using Lattice

In a right triangle with g the right angle, a = 69.2° and c = 28.3. What is b?

so


so...
b=10.05

Solve: -5=-6+2e^(-2x)

:) 

16^(x+4)=8^(3x-2)

For this example our strategy is to make the bases equal, then we can set the exponents equal:

so x=22/5 

The inequality x<5 is a statement about the size of x compared to 5 

adding/subtracting...
x+1<5+1
x+2<5+2
x+a<5+a 
multiples of both sides...
2x<10
2x<15
bx<5b 
In fact many reversible things we do to the left (as well as the right side) are possible :)

Find the slope of the following line. 4y=x+4

The slope is the coefficient of the x term when the equation is in slope-intrcept form. Therefore our slope is 1/4

what is 3 square root of 2 + square root of 8

Find the determinants, Dx, and Dy given: {3x-y=7 , -5x+4y=-2}

Dx=
| 7 -1|
|-2 4|
which is equal to
Dx=7*4-(-2)(-1)=28-2=26

Dy=
| 3 7 |
|-5 -2|
which is equal to
Dy=(3)(-2)-(-5)(7)=-6+35=29

The sum of the arithmetic is 192 with a last term of 27 and a common difference of 2. Find the number of terms.

Setting up our equations we find:

 and 

Solving the system by substitution leads to two possible solutions, both valid.
, 

or
,