Question

Evaluate the following expressions using the given values. a. \(a b^{2}+4 c\) for \(a=3, b=-5, c=-3\) b. \((5 x+3 y)(2 x-y)\) for \(x=-4, y=6\) c. \(-5 c\left(14 c d-3 d^{2}\right)\) for \(c=3, d=-2\) d. \(\frac{3 a x-4 c}{4 a c}\) for \(a=-2, c=4, x=-8\)

Short answer

Answer: The final values of the expressions are a. 63, b. 28, c. 1440, and d. 2.

Step-by-step solution

Substitute the given values

We will start by plugging the given values into the given expressions. a. \((3)(-5)^{2}+4(-3)\) b. \((5(-4)+3(6))(2(-4)-6)\) c. \(-5(3)\left(14(3)(-2)-3(-2)^{2}\right)\) d. \(\frac{3(-2)(-8)-4(4)}{4(-2)(4)}\)

Perform the arithmetic operations

Now, let's perform the arithmetic operations. a. \((3)(25)+(-12) = 75-12\) b. \((-20+18)(-8-6) = (-2)(-14)\) c. \(-15\left(-84-12\right) = -15(-96)\) d. \(\frac{-48-16}{-32} = \frac{-64}{-32}\)

Simplify the expressions

Finally, we will simplify the expressions and obtain the final values. a. \(75-12 = 63\) b. \((-2)(-14) = 28\) c. \(-15(-96) = 1440\) d. \(\frac{-64}{-32} = 2\) So, the final values are: a. \(63\) b. \(28\) c. \(1440\) d. \(2\)