Question

Simplify
-5n2+2(7m3+2n2)

Answer 1

\[-5n ^{2}+2(7m ^{3}+2n ^{2})\]

Answer 2

so from .....
\[-5n ^{2}+14m ^{3}+4n ^{2}\]
now simplify that

Answer 3

-1n2+14m3 ?

Answer 4

Step 1 :

Multiply 2 by 2n^2+7m^3

Factor: 2n^2+7m^3

A sum of two perfect cubes, a^3 + b^3 can be factored into :
(a+b) • (a^2-ab+b^2)
Checking : (a+b) • (a^2-ab+b^2) =
a^3-a^2b+ab2+ba^2-b^2a+b^3 =
a^3+(a^2b-ba^2)+(ab^2-b^2a)+b^3=
a3+0+0+b3=
a3+b3

Check : 2 is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes


Equation at the end of step 1 :

(0 - (5 • (n^2))) + 2 • (2n^2 + 7m^3)
Step 2 :

Simplify -5n^2 + 2•(2n^2+7m^3)
factor as a Difference of Cubes:

2.1 Factoring: 14m^3-n^2

Theory : A difference of two perfect cubes, a^3 - b^3 can be factored into
(a-b) • (a^2 +ab +b^2)

Proof : (a-b)•(a^2+ab+b^2) =
a^3+a^2b+ab^2-ba^2-b^2a-b^3 =
a^3+(a^2b-ba^2)+(ab^2-b^2a)-b^3 =
a^3+0+0+b^3 =
a^3+b^3

Check : 14 is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes


Answer:

14m^3 - n^2

Answer 5

ok thanks :)

Answer 6

sorry its long xD kinda overexagerated