gistfile1.txt

Unit 1 Key Questions

1
(5x + 3)^2 - (4x + 1)(6 - x)
=25x^2 + 30x + 9 - (24x - 4x^2 + 6 - x)
=25x^2 + 30x + 9 - 24x + 4x^2 - 6 + x
= 29x^2 + 7x + 3

2
a
-6\s{80} + 2\s{75} - 8\s{245} - 14\s{108}
=-6\s{16 * 5} + 2\s{25 * 3} - 8\s{49 * 5} - 14\s{36 * 3}
=-6(4\s{5}) + 2(5\s{3}) - 8(7\s{5}) - 14(6\s{3})
=-24\s{5} + 10\s{3} - 56\s{5} - 84\s{3}
=-80\s{5} - 74\s{3}
=~-307.06

b
(2\s{5} - 4\s{6})(3\s{3}+8\s{2})
=(2\s{5})(3\s{3}) + (2\s{5})(8\s{2}) - (4\s{6})(3\s{3}) - (4\s{6})(8\s{2})
=6\s{15} + 16\s{10} - 12\s{18} - 32\s{12}
=6\s{15} + 16\s{10} - 12\s{9 * 2} - 32\s{4 * 3}
=6\s{15} + 16\s{10} - 36\s{2} - 64\s{3}
=~-87.93

3
a
((x^2 - x - 6) / (x^2 - 4)) \d ((x^2 - 2x + 1) / (x^2 - 1))
=(((x+2)(x-3)) / ((x-2)(x+2))) \d (((x-1)(x-1)) / ((x-1)(x+1)))
=(((x+2)(x-3)) / ((x-2)(x+2))) * (((x-1)(x+1)) / ((x-1)(x-1)))
=((x-3) / (x-2)) * ((x+1) / (x-1))
=((x-3)(x+1)) / ((x-2)(x-1))
=(x^2 - 2x - 3) / (x^2 - 3x + 2)

b
((2x) / (9x^2 + 15x)) - (8 / (3x + 5))
=((2x) / (9x^2 + 15x)) - ((3x * 8) / (3x(3x + 5)))
=((2x) / (9x^2 + 15x)) - (24 / (9x^2+15x))
=((2x - 24x) / (9x^2 + 15x))
=(-22x) / (9x^2 + 15x)