Question

If A=-3+5t,B=4-2t, and C=1+6t, where i is the imaginary unit, then A-BC equals

Answer 1

To find A-BC, multiply B and C to obtain BC, then subtract BC from A. After simplifying, the final expression for A-BC equals 12t^2 - 17t - 7.

Step-by-step explanation:

The question involves finding the expression for A-BC, where A, B, and C are given algebraic expressions in terms of a variable t, and i is the imaginary unit. First, we must calculate the value of BC:

• B = 4-2t
• C = 1+6t
• BC = (4-2t)(1+6t)

We then multiply these two expressions to find BC:

1. BC = 4(1) + 4(6t) - 2t(1) - 2t(6t)
2. BC = 4 + 24t - 2t - 12t2
3. BC = 4 + 22t - 12t2

Next, we calculate A-BC by substituting the value of A and BC:

• A = -3+5t
• A-BC = (-3+5t) - (4 + 22t - 12t2)

Now we expand and simplify the expression:

1. A-BC = -3 + 5t - 4 - 22t + 12t2
2. A-BC = 12t2 - 17t - 7

So, the final expression for A-BC equals 12t2 - 17t - 7.