Expand and state your answer as a polynomial in standard form.
left parenthesis, 3, x, minus, y, to the power 5 , right parenthesis, squared
(3x−y
5
)
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
1 answer
To expand the expression \( (3x - y^5)^2 \) and present it in standard polynomial form, we follow the process similar to the example you provided.
Step 1: Write the expression
We start with:
\[
(3x - y^5)(3x - y^5)
\]
Step 2: Expand the expression
Using the distributive property (also known as FOIL for binomials), we will multiply each term of the first binomial by each term of the second binomial:
First: \( (3x)(3x) = 9x^2 \)
Outer: \( (3x)(-y^5) = -3xy^5 \)
Inner: \( (-y^5)(3x) = -3xy^5 \)
Last: \( (-y^5)(-y^5) = y^{10} \)
Now putting all these together, we have:
\[
9x^2 - 3xy^5 - 3xy^5 + y^{10}
\]
Step 3: Combine like terms
Combine the like terms (\(-3xy^5\) and \(-3xy^5\)):
