Multiply (x-1)(x^2-2x+4)
Simplify (2+i)(2-i)
Multiply x by each term in x^2-2x+4
Then multiply -1 by each term in x^2-2x+4.
Then add up all terms.
Then collect all the x^3, x^2, x and constant terms. For example, you should have two x^2 terms: -2x^2 and -x^2. Combine them and write them as -3x^2.
(2+i)(2-i) = 4 - i^2 = 4 - (-1) = ?
Just to see if I calculated correctly the first problem = x^3-3x^2+6x-4.
Then the answer to the other problem is 5.
To multiply the two polynomials, (x-1) and (x^2-2x+4), you can use the distributive property.
Step 1: Distribute (x-1) to each term of (x^2-2x+4):
(x-1)(x^2-2x+4) = x(x^2-2x+4) - 1(x^2-2x+4)
Step 2: Simplify each product:
= x^3 - 2x^2 + 4x - x^2 + 2x - 4
Step 3: Combine like terms:
= x^3 - 3x^2 + 6x - 4
Therefore, (x-1)(x^2-2x+4) simplifies to x^3 - 3x^2 + 6x - 4.
To simplify the expression (2+i)(2-i), you can use the distributive property as well.
Step 1: Distribute (2+i) to each term of (2-i):
(2+i)(2-i) = 2(2-i) + i(2-i)
Step 2: Simplify each product:
= 4 - 2i + 2i - i^2
Now, recall that i^2 is defined as -1:
= 4 - 2i + 2i - (-1)
= 4 - 2i + 2i + 1
Step 3: Combine like terms:
= 5
Therefore, (2+i)(2-i) simplifies to 5.