Question

How do you expand ${(y - {x^2})^3}$ ?

Answer 1

Hint:
To expand the above question, we will solve the whole cube of the given term with the help of identities and then put the given values into the identities. In the first method, we will use the identity in which two numbers are added and in the second method, we use the identity in which two numbers are subtracted.

Formula used:
${(a + b)^3} = {a^3} + 3{a^2}b + 3a{b^2} + {b^3}$

Complete step by step solution:
As per question, we have to expand a given term, as we observe there is a whole cube in the term, so we will simplify that by using the identity given below.
${(a + b)^3} = {a^3} + 3{a^2}b + 3a{b^2} + {b^3}$
Here, we will consider
$a = y$
And $b = - {x^2}$
${(y - {x^2})^3} = {y^3} - 3{y^2}{x^2} + 3y{x^4} - {x^6}$

Hence, this is the expanded form of above question.

Note:
Second method to solve above question:
Formula used:
${(a - b)^3} = {a^3} - 3{a^2}b + 3a{b^2} - {b^3}$