Question

question 1 of 10
the binomial expansion of \\(\left(x + y^2\
ight)^2\\) is ______.

a. \\(x^2 + 2xy + y^2\\)
b. \\(x^2 + 2xy^2 + y^4\\)
c. \\(x^2 + 2xy^2 + y^2\\)
d. \\(x^2y^2 + 2xy^3 + y^4\\)

Explanation:

Step1: Apply binomial square formula

The formula for $(a + b)^2$ is $a^2 + 2ab + b^2$. Here, $a = x$ and $b = y^2$.

Step2: Calculate each term

First term: $a^2 = x^2$
Second term: $2ab = 2 \cdot x \cdot y^2 = 2xy^2$
Third term: $b^2 = (y^2)^2 = y^4$

Step3: Combine terms

Sum the terms: $x^2 + 2xy^2 + y^4$

Answer:

B. $x^2 + 2xy^2 + y^4$