To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -48 as well and sum (Inside, Outside) to equal 2. For this problem, those two numbers are -6 and 8. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 2y - 48
y² + (-6 + 8)y + (-6 x 8)
(y - 6)(y + 8)

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

You need to find the value of c so solve the first equation in terms of x:

8c + x = -8
x = -8 - 8c

then substitute the result (-8 - 8c) into the second equation:

8c + 2(-8 - 8c) = -2
8c + (2 x -8) + (2 x -8c) = -2
8c - 16 - 16c = -2
8c - 16c = -2 + 16
-8c = 14
c = \( \frac{14}{-8} \)
c = -1\(\frac{3}{4}\)

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(3 + 4)(4)
a = ½(7)(4)
a = ½(28) = \( \frac{28}{2} \)
a = 14

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(8a)(2ab) - (5a²)(7b)
(8 x 2)(a x a x b) - (5 x 7)(a² x b)
(16)(a¹⁺¹ x b) - (35)(a²b)
16a²b - 35a²b
-19a²b