Final answer:
To find 5(3x-11)^2, expand the binomial using the FOIL method and then multiply the result by 5, which yields the final expanded polynomial 45x^2 - 330x + 605.
Step-by-step explanation:
To multiply the given polynomials, we have 5(3x-11)2. First, we need to handle the exponent by expanding, which means we square the binomial (3x-11) and then multiply the result by 5.
Step 1: Expand the square of the binomial:
- (3x - 11)2 = (3x - 11)(3x - 11)
Step 2: Apply the FOIL method (First, Outer, Inner, Last) to multiply the two binomials:
- First: (3x)(3x) = 9x2
- Outer: (3x)(-11) = -33x
- Inner: (-11)(3x) = -33x
- Last: (-11)(-11) = 121
Now combine like terms:
- 9x2 - 33x - 33x + 121 = 9x2 - 66x + 121
Step 3: Finally, multiply this result by 5:
- 5(9x2 - 66x + 121) = 45x2 - 330x + 605
The final answer is 45x2 - 330x + 605.