The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

b² - 15b + 51 = -b + 2
b² - 15b + 51 - 2 = -b
b² - 15b + b + 49 = 0
b² - 14b + 49 = 0

Next, factor the quadratic equation:

b² - 14b + 49 = 0
(b - 7)(b - 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, (b - 7) must equal zero:

If (b - 7) = 0, b must equal 7

So the solution is that b = 7

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(7²) + 2π(7 x 8)
sa = 2π(49) + 2π(56)
sa = (2 x 49)π + (2 x 56)π
sa = 98π + 112π
sa = 210π

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 6 x 4 = \( \frac{24}{2} \) = 12

A trapezoid is a quadrilateral with one set of parallel sides.

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 9)(y - 8)
(y x y) + (y x -8) + (9 x y) + (9 x -8)
y² - 8y + 9y - 72
y² + y - 72