(2k + 3)(k - 1
1. 2k2 + k - 3
2. 2k2 + k + 2
3. 2k2 - k - 3
4. 2k2 - k + 2
explain
To expand (2k + 3)(k - 1), we use the distributive property:
2k(k - 1) + 3(k - 1)
Simplifying each term:
2k² - 2k + 3k -3
Combining like terms:
2k² + k - 3
Therefore, the correct answer is option 1: 2k² + k - 3.
To expand the expression (2k + 3)(k - 1), we can use the distributive property. This property states that for any numbers a, b, and c, (a + b)(c) is equal to ac + bc.
Applying this property to our expression, we get:
(2k + 3)(k - 1) = 2k(k - 1) + 3(k - 1)
Now we can simplify each term separately:
1. 2k(k - 1)
To simplify, we distribute 2k to both terms in the parentheses:
2k * k = 2k^2
2k * -1 = -2k
So, 2k(k - 1) simplifies to 2k^2 - 2k.
2. 3(k - 1)
Again, we distribute 3 to both terms in the parentheses:
3 * k = 3k
3 * -1 = -3
So, 3(k - 1) simplifies to 3k - 3.
Now we combine the simplified terms:
(2k + 3)(k - 1) = 2k^2 - 2k + 3k - 3
Simplifying further by combining like terms:
2k^2 + k - 3
So, the expansion of (2k + 3)(k - 1) is 2k^2 + k - 3. This corresponds to option 1.