Expand and state your answer as a polynomial in standard form.left bracket, 3, x, to the power 5 , minus, y, cubed, right bracket, squared(3x 5 −y 3 ) 2
Question
Expand and state your answer as a polynomial in standard form.left bracket, 3, x, to the power 5 , minus, y, cubed, right bracket, squared(3x 5 −y 3 ) 2
Solution
The expression you provided is (3x^5 - y^3)^2. To expand this, we use the formula (a - b)^2 = a^2 - 2ab + b^2. Here, a is 3x^5 and b is y^3.
Step 1: Square a (3x^5)^2 = 9x^10 Step 2: Multiply a and b and double the result 2 * 3x^5 * y^3 = 6x^5y^3 Step 3: Square b (y^3)^2 = y^6
Now, put it all together: 9x^10 - 6x^5y^3 + y^6
So, the expanded form of (3x^5 - y^3)^2 is 9x^10 - 6x^5y^3 + y^6. This is a polynomial in standard form.
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