Question

Please Help Me

Answer 1

Please explain the highlighted steps I do not understand it

Answer 2

OK.

The 1st highlighted one, you got by 372/12 = 31

The 2nd highlighted one, you obtained by factoring of r^3 - 1

We have a trick:\[a^3 - b^3 = (a-b)(a^2+ab+b^2)\]

That's the explanation.

Answer 3

on the first one it divided both sides by 12 then on the second one it broke down (r^3-1)

Answer 4

How did it break down (r^3-1) thats what I do not understand

Answer 5

I explained above, that's a trick to do maths

Answer 6

but i thought it was a^2+2ab+b^2

Answer 7

OK, let's try together step by step.

\[a^3 - b^3 = a^3 - a^2b +a^2b - b^3 = a^2 (a -b) + b(a^2-b^2)\]
\[= a^2(a-b) + b(a-b)(a+b) = (a-b)(a^2 +ab+b^2)\]

Does it make sense? @waheguru

Answer 8

The factorization of a difference of cubes is:

\(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\)

Answer 9

yea get it thanks

Answer 10

The term 2ab shows in a perfect square trinomial. In the factorization of a sum of two cubes or difference of two cubes, you get ab.

Keep these in mind. In fact, it is worthwhile memorizing them.



\(a^2 + 2ab + b^2 = (a + b)^2 \)

\(a^2 - 2ab + b^2 = (a - b)^2 \)

\( a^2 - b^2 = (a + b)(a - b) \)

\(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)

\(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\)