Of course! I'd be happy to help you.
To find the product of two binomials like the ones given, you can use the FOIL method. FOIL stands for First, Outer, Inner, Last, which represents the order in which you multiply the terms of the two binomials.
Let's start with question 4:
(3x+4)(x - 2)
F: Multiply the first terms of each binomial: 3x * x = 3x^2
O: Multiply the outer terms of each binomial: 3x * -2 = -6x
I: Multiply the inner terms of each binomial: 4 * x = 4x
L: Multiply the last terms of each binomial: 4 * -2 = -8
Now, we combine these results to simplify the expression:
3x^2 - 6x + 4x - 8
Combine like terms:
3x^2 - 2x - 8
Therefore, the answer to question 4 is option A: 3x^2 - 2x - 8.
Now let's move on to question 5:
(2y-1)(4y-3)
F: Multiply the first terms of each binomial: 2y * 4y = 8y^2
O: Multiply the outer terms of each binomial: 2y * -3 = -6y
I: Multiply the inner terms of each binomial: -1 * 4y = -4y
L: Multiply the last terms of each binomial: -1 * -3 = 3
Now, we combine these results to simplify the expression:
8y^2 - 6y - 4y + 3
Combine like terms:
8y^2 - 10y + 3
Therefore, the answer to question 5 is option C: 8y^2 - 10y + 3.
I hope this helps! Let me know if you have any other questions.