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n200080 [17]
3 years ago
9

1. Create an expression, containing at least two variables, that can be factored using the sum of two cubes identity.

Mathematics
1 answer:
podryga [215]3 years ago
8 0
Remember that the sum of tow cubes identity is: a^3+b^3=(a+b)(a^2-ab+b^2)
So, to create our expression<span>, containing at least two variables, that can be factored using the sum of two cubes, we just need to replace </span>a and b with tow monomials with a different variable:
a=x and b=y
Lets replace those values in our identity: 
x^3+y^3

Now that we have our expression, lets factor it using the sum of two cubes identity:
x^3+y^3=(x+y)(x^2-xy+y^2)
To verify if the factored form of our expression (right hand side) is equivalent to the original form (left hand side), we are going to expand the right hand side:
x^3+y^3=(x+y)(x^2-xy+y^2)
x^3+y^3=x^3-x^2y+xy^2+x^2y-xy^2+y^3
x^3+y^3=x^3+x^2y-x^2y+xy^2-xy^2+y^3
x^3+y^3=x^3+y^3

Since both sides of the equation are equal, we can conduce that the factored form of our expression is equivalent to the original expression.

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