Question

10b^3-40b=0

Answer 1

Awesome, \(10b^3 - 40b = 0\) is our question, can you think of a common factor to divide by to simplify this equation (hint. it rhymes with hen)

Answer 2

i think it might be 10?

Answer 3

Good stuff, so what does dividing everything by 10 give

Answer 4

b^2-4b

Answer 5

(I thought originally it was 10b^3??) But if not, that's right. Now we can factorise by b

Answer 6

oh sorry

Answer 7

it was

Answer 8

Ok no worries, so from \(b^3-4b=0\) we can take out a b, because every term in our equation contains a b. So what will you get if you take out a b?

Answer 9

b(b^2-4)=0?

Answer 10

Yeah!! And now for the final step of actually finding what b is. Because the original question was a cubic (b^3) we can expect to get 3 answers for b. Can you think of any at the moment?

Answer 11

im not sure how to find any

Answer 12

oh wait 0 is one of them

Answer 13

Ok no problem, let's split our equation up into the different bits. We know that \(b(b^2 - 4) = 0\) Looking at this equation we can split it into the different brackets. Meaning we can write\[b=0\]and \[b^2-4=0\]We are allowed to do this because we know that one or other of these parts must be equal to 0 because anything multiplied by 0 is equal to 0. With me so far?

Answer 14

im with you

Answer 15

Fantastic! So we already know that \(b=0\) is one solution. What about the second equation?

Answer 16

2,-2?

Answer 17

BOOM!!! Bang on the money! That is correct! So to conclude \(b=0,-2,2\)

Answer 18

Hope that helped!

Answer 19

ok sweet thank you! I hope you do this for a living you're really good at it!