(2y – 1)(4y – 3)
A. –2y + 3
B. 8y2 – 10y – 3
C. 8y2 – 10y + 3
D. 8y2 – 2y + 3
To expand this expression, we can use FOIL (First, Outer, Inner, Last) method.
First: 2y times 4y gives 8y^2
Outer: 2y times -3 gives -6y
Inner: -1 times 4y gives -4y
Last: -1 times -3 gives 3
Putting it all together, we get:
(2y – 1)(4y – 3) = 8y^2 - 6y - 4y + 3 = 8y^2 - 10y + 3
Therefore, the answer is C. 8y^2 – 10y + 3.
To expand the expression (2y – 1)(4y – 3), we can use the distributive property. This property states that for any real numbers a, b, and c, (a + b)(c) = ac + bc.
Here, we have two binomials, (2y – 1) and (4y – 3), so we can expand the expression as follows:
(2y – 1)(4y – 3)
= (2y)(4y) + (2y)(-3) + (-1)(4y) + (-1)(-3)
= 8y^2 - 6y - 4y + 3
= 8y^2 - 10y + 3
Therefore, the expanded form of (2y – 1)(4y – 3) is 8y^2 - 10y + 3.
The correct option is C. 8y^2 - 10y + 3.
To simplify the expression (2y – 1)(4y – 3), we can use the distributive property:
(2y – 1)(4y – 3) = 2y(4y) + 2y(-3) - 1(4y) - 1(-3)
Now, multiply each term:
= 8y^2 - 6y - 4y + 3
Combine like terms:
= 8y^2 - 10y + 3
Therefore, the simplified expression is 8y^2 - 10y + 3.
So, the correct answer is:
C. 8y^2 - 10y + 3.