adding expoent?

Question

is x^3 + y ^3 = (x+y)^3?

x^3 + x^4 =? is it possible to simplfiy?

Answer 1

No

x³ + y³ = (x+y)(x²-xy+y²)
(x+y)³ = x³ + 3x²y + 3xy² + y³
If you have any doubts about this, try substituting x=1, y=2 or any other non-zero values of your choice.


x³ + x^4 cannot be simplified any further. It can be factored to x³(1+x).

Answer 2

a) is x^3 + y ^3 = (x+y)^3?
No. First, of all the addition of exponents applies only in the case of MULTIPLYING two powers with the same bases and not in adding two powers (whether with the same base or different bases).
Two powers with different bases can not be combined. You can only indicate their sum. Hence, in your example it is only
x^3 + y^3 and not (x + y)^3.

Ib) x^3 + x^4 =? is it possible to simplfiy?
One common error among students is to ADD the two powers. Although they have the same bases, you can not add the two powers and say 2x^7. Again, exponents can be added only in the case of multiplication of two powers with the same bases.
You can factor out the greatest common factor:
x^3(1 + x) ANS


teddy boy

Answer 3

No!

Let x=2 and y=3
2^3=8
3^3=27
8+27=35

2+3=5
5^3=125
125 does not equal 35

That's a no-no.

Answer 4

no to the first
only by factoring x^3(1+x)

Answer 5

x^3 + y^3 = (x+y)(x^2 - xy + y^2)

The 2nd expression cannot be simplified further.

Answer 6

x^3 + y ^3 = xxx + yyy

(x+y)^3 = (x+y)(x+y)(x+y) = (x+y)(x^2+2xy+y^2) =
(x^3y+2x^2y^2+xy^3)

So the answer to your first question is no.

The answer to your second question is also no.