exponents i forgot this from a long time ago?

Question

simplify

(4x+5)^2?? please explain

6x^2-(8x-9x^2)=2x-3x^2

(4m^3-2m+1)-(5m^3+4m+6)

THE SECOND ONE IS SUPPOSED TO BE
6x^2-(8x-9x^2)+2x-3x^2

Answer 1

Question 1
(4 x + 5) (4 x + 5)
16 x ² + 20 x + 20 x + 25
16 x ² + 40 x + 25

Question 2
6 x ² - 8 x + 9 x ² + 2 x - 3 x ²
12 x ² - 6 x
(6 x) (2 x - 1)

Question 3
- m ³ - 6 m - 5

Answer 2

1) When a single term is raised to a power, you just multiply that number together as many times as its power. (ex. 2x^2 = 2*2*x*x = 4x^2) But in this case, a single term is not being raised, a binomial (two terms) is. In this case you are multiplying the whole binomial by itself:

(4x+5)(4x+5). You will have to multiply this out by multiplying each term to all other terms (you should get a trinomial):

4x*4x + 4x*5 + 5*4x + 5*5

Simplifies to:
16x^2 + 40x + 25 (your answer)

(You can also use the FOIL method if you know it.)


2) Start out by removing the parenthesis. To do this, you need to notice that this expression also looks like this...

6x^2-1(8x-9x^2)+2x-3x^2

Now that you recognize that there is a negative one multiplied to the binomial in the parenthesis, you must distribute it.

6x^2-8x+9x^2+2x-3x^2 ( - * - = +)

Now combine like terms (x^2 and x)

6x^2 - 3x^2 + 9x^2 - 8x + 2x

Simplifies to:

12x^2 - 6x (your answer)


3) Again you will need to take notice that there is a 1 multiplied with the first trinomial and a -1 multiplied with the second.

1(4m^3-2m+1) -1(5m^3+4m+6)

Then distribute the 1 and -1.

4m^3 - 2m + 1 - 5m^3 - 4m - 6.

Now combine like terms (x^3, x, and the numbers)

4m^3 - 5m^3 - 2m - 4m + 1 - 6.

Then simplify:
-m^3 - 6m - 5 (your answer)

Answer 3

1. (4x+5)^2 requires squaring the expression in the parenthesis: (4x+5)*(4x+5) = 16x^2 +40x + 25. I don't see how to reduce it any further since the numbers do not have any common denominator.

2. The second equation is 6x^2 -8x +9x^2+2x-3x^2 or 15x^2-6x -3x^2 or 12x^2-6x or 6(2x^2-x).

3. (4m^3-2m+1)-(5m^3+4m+6) = 4m^3-2m+1-5m^3-4m-6 which becomes -m^3-6m-5

Answer 4

write these answers out on paper so you can see them more clearly. Brief notes are within the brackets.

(4x + 5)^2 [expand it]
=(4x +5) (4x+5) [multiply out]
=16x^2 + 18x +25

6x^2 -(8x-9x^2) = 2x -3x^2 [bring the equation to the left side only]
=6x^2 + 9x^2 + 3x^2 - 8x - 2x = 0 [simplify]
=18x^2 - 10x = 0 [factor, bring the LCD to the front]
=2x(9x-5) = 0

(4m^3-2m+1)-(5m^3+4m+6) [simplify the brackets]
= 4m^3 - 2m +1 - 5m^3 - 4m - 6 [group together the common terms]
=4m^2 - 5m^3 - 2m - 4m + 1 - 6 [simplify]
= -1m^2 - 6m - 5 [bring the LCD out in front]
= -(m^2 + 6m + 5) [factor]
= -[(x + 5) (x+1)]

Answer 5

1st answer:
= (4x + 5) * 4x
= 16x^2 + 20x

= (4x + 5) * 5
= 20x + 25

= 16x^2 + 20x + 20x + 25
= 16x^2 + 40x + 25

2nd answer:
= 6x^2 - (8x - 9x^2) + (2x - 3x^2)
= 6x^2 - 8x + 9x^2 + 2x - 3x^2
= 12x^2 - 6x

3rd answer:
= (4m^3 - 2m + 1) - (5m^3 + 4m + 6)
= 4m^3 - 2m + 1 - 5m^3 - 4m - 6
= -m^3 - 6m - 5

Answer 6

1. 16x^2+40x+25

2. 6x^2-8x+9x^2 = 2x-3x^2
15x^2-8x-2x+3x^2 = 0
18x^2-10x = 0

Answer 7

(4x+5)^2 is equal to (4x+5)(4x+5)
therefore we use FOIL method First, Outer, Inner and Last term.
Fist term 4x and 4x = 16x^2
Outer term 4x and 5 = 20x
Inner term 5 and 4x = 20x
Last term 5 and 5 = 25
then add: 16x^2 +20x +20x +25
therefore the ans. is = 16x^2 +40x +25

Answer 8

::Q1::
based on (mx+n)^2 = (mx+n)(mx+n), we get:

(4x+5)(4x+5)........... expand this and you get:
16x^2+20x+20x+25....... simplify this and you get:

16x^2+40x+25

::Q2::
expand and the whole equation becomes:
6x^2-8x+9x^2+2x-3x^2...................collect like factors:
12x^2-6x...........................factor out common factor:
6(2x^2-x)

::Q3::
this is the similar to Q2:

expand: 4m^3-2m+1-5m^3-4m-6
like terms: -m^3-6m-5
beautify: -(m^3+6m+5)

Answer 9

(4x+5)(4x+5)=16x^2+40x+25
Since it is squared, it's basically itself multiplied by itself.
Once written, use the FOIL method ((1in * 2in) + (1in * 2out) + (1out * 2in) + (1out *2out)

12x^2+6x
Add all the like terms together

m^3-6m-5
Add like terms together

Answer 10

(4x+5)(4x+5) then multiply it out and symplify