Question

Expand and state your answer as a polynomial in standard form.
left parenthesis, 4, x, cubed, plus, y, to the power 4 , right parenthesis, squared
(4x
3
+y
4
)
2







Solve the problem just like the example below
⬇️
Expand and state your answer as a polynomial in standard form.
left parenthesis, 3, x, to the power 5 , plus, y, to the power 5 , right parenthesis, squared
(3x
5
+y
5
)
2
For binomials left parenthesis adding or subtracting right parenthesis
For binomials (adding or subtracting)
we must expand the power.
we must expand the power.
left parenthesis, 3, x, to the power 5 , plus, y, to the power 5 , right parenthesis, left parenthesis, 3, x, to the power 5 , plus, y, to the power 5 , right parenthesis
(3x
5
+y
5
)(3x
5
+y
5
)
left parenthesis, 3, x, to the power 5 , right parenthesis, left parenthesis, 3, x, to the power 5 , right parenthesis, plus, left parenthesis, 3, x, to the power 5 , right parenthesis, left parenthesis, y, to the power 5 , right parenthesis, plus, left parenthesis, 3, x, to the power 5 , right parenthesis, left parenthesis, y, to the power 5 , right parenthesis, plus, left parenthesis, y, to the power 5 , right parenthesis, left parenthesis, y, to the power 5 , right parenthesis
(3x
5
)(3x
5
)+(3x
5
)(y
5
)+(3x
5
)(y
5
)+(y
5
)(y
5
)
9, x, to the power 10 , plus, 3, x, to the power 5 , y, to the power 5 , plus, 3, x, to the power 5 , y, to the power 5 , plus, y, to the power 10
9x
10
+3x
5
y
5
+3x
5
y
5
+y
10
9, x, to the power 10 , plus, 6, x, to the power 5 , y, to the power 5 , plus, y, to the power 10
9x
10
+6x
5
y
5
+y
10

Answer 1

To expand and rewrite \((4x^3 + y^4)^2\) as a polynomial in standard form, we follow a similar approach to the example you provided.

1. **Identify the expression**:
\[
(4x^3 + y^4)^2
\]

2. **Expand the power**:
\[
(4x^3 + y^4)(4x^3 + y^4)
\]

3. **Apply the distributive property (also known as the FOIL method for binomials)**:
- First: \((4x^3)(4x^3) = 16x^{6}\)
- Outer: \((4x^3)(y^4) = 4x^3y^4\)
- Inner: \((y^4)(4x^3) = 4x^3y^4\)
- Last: \((y^4)(y^4) = y^{8}\)

4. **Combine the results**:
\[
16x^{6} + 4x^3y^4 + 4x^3y^4 + y^8
\]

5. **Combine like terms**:
\[
16x^{6} + 8x^3y^4 + y^8
\]

6. **Write the final answer in standard form**:
\[
16x^{6} + 8x^3y^4 + y^8
\]

Thus, the expanded form of \((4x^3 + y^4)^2\) is:
\[
\boxed{16x^{6} + 8x^3y^4 + y^8}
\]