Question

Choose the correct simplification of the expression −3x2(5x − 4x2 − 6).

−7x4 + 2x3 − 9x2
12x4 − 15x3 + 18x2
12x4 + 15x3 + 18x2
−12x4 + 15x3 − 18x2

Can someone help me understand this?

Answer 1

@phi

Answer 2

you should re-order this part
(5x − 4x^2 − 6)
so the largest exponent is first:
(-4x^2 + 5x - 6)


now multiply each term by −3x^2

−3x^2 (-4x^2 + 5x - 6)

do you know what -3x^2 * -4x^2 is ?

Answer 3

remember
-3x^2 * -4x^2
means
-3*-4*x^2 *x^2
what is -3 * -4 ?

Answer 4

12

Answer 5

12^2 or 12^4?

Answer 6

-3*-4 is 12
so
-3*-4*x^2*x^2 is the same as
12*x^2*x^2

remember x^2 means x*x
so we could write
12*x^2*x^2 is the same as 12*x*x*x*x

Answer 7

most people use the "short-cut" way to write x*x*x*x
(using a "little 4" in the upper right of x)

Answer 8

Ok. Do you add or multiply the exponents?

Answer 9

it's easier to remember, if you get the idea that the "exponent" way is just a short cut.
for example: x^1 * x^2 means x * x * x
and x*x*x is x^3 using the "short-cut"
notice the exponent 3 is 1+2

Answer 10

if you can't remember any of that, and you see
x^2 *x^2
write it as x*x * x*x
now count the x's
and use the short-cut way to write

Answer 11

Ok, but my teacher has to talk to me and ask questions. 1 might be, if you multiply exponents do you add them or multiply them? I just wanna know for the future

Answer 12

yes. And I am saying you will remember the answer better if it "makes sense"
and it will make sense if you can figure it out. And I know you can figure it out.
Just go slow with this problem:
x^1 * x^2 = x * x*x = x^3
notice the 3 is the sum of 1+2

Answer 13

−3x^2 (-4x^2 + 5x - 6) the first term will be 12x^4
now what do you get for the next term: -3x^2 * 5x ? any idea ?

Answer 14

15x^2?

Answer 15

what is -3*5 ?

Answer 16

-15 sorry XD -15x^2

Answer 17

-3x^2 * 5x
is
-3*x*x * 5*x
or re-arranging it
-3*5*x*x*x
now simplify -3*5
and write x*x*x using exponents

Answer 18

x^3

Answer 19

yes, that means
-3x^2 * 5x = -15x^3

Answer 20

the last term is
−3x^2 * -6

Answer 21

−3x^2 * -6
re-arrange it as
-3*-6*x*x

Answer 22

-18x^2

Answer 23

you have trouble with minus signs:
if you multiply minus times minus you get plus

Answer 24

Wait
18x^2 I just noticed

Answer 25

I didnt see the 6 was -.. sorry :P

Answer 26

so the answer is B?

Answer 27

ok, now you have the answer
−3x^2 (-4x^2 + 5x - 6) = 12x^4 -15x^3 +18x^2

Answer 28

Thank you :D