1) It's (8x - 3)(8x + 3).

2) Let n be the number you're looking for. Then:

n² + (n+1)² = 61

n² + n² + 2n + 1 = 61

2n² + 2n - 60 = 0

2(n-5)(n+6) = 0

n = -6 and n = 5.

So, both -6, -5 and 5, 6 will work.

3) (3z+2)(5z-4)

4) (5x-3)² = 18x² + 1

25x² - 30x + 9 = 18x² + 1

7x - 30x + 8 = 0

(x-4)(7x - 2) = 0

x=4 and x = (2/7)

The integer solution is x=4.

5) The total area of the page is 12*18 = 216 cm². The printed material covers 40 cm², leaving 176 for the margins. Set up an equation for the margins and solve it.

Let w = the width of the margins. Then,

12w + 12w + 2(18-2w)w = 176

-4w² + 60w - 176 = 0

-4(w-11)(w-4) = 0

w = 11 or w = 4

Two widths would work, but 11 is almost 12, which is one of the dimensions of the page, so that's probably not the best choice. Let's check it with 4:

48 + 48 + 40 + 40 = 176

6) You're correct on this one.

Note that I used a calculator to factor some of those quadratics, since factoring isn't one of my strong points. Lacking that, I'd resort to the quadratic formula.

Note also that when factoring, I always have to expand my factored expression to check and see if it's right.