a.
33x³y⁴ - 22x²y² + 11x²y =
11x²y(3xy³ - 2y + 1) =
11x²y(1 + y(3xy² - 2))
b.
y(2x - 3) + 4(2x - 3) =
(2x - 3)(y + 4)
c.
4x³y⁴ - 17y⁴ + 35x¹²y⁷ =
y⁴(4x³ - 17 + 35x¹²y³) =
y⁴(x³(4 + 35x⁹y³) - 17)
d.
(x² + 2x²) - 9 =
3x² - 9 =
3(x² - 3) =
e. f.
(x - y)² -2(x - y) - 8 =
(x - y + 2)(x - y - 4)
g.
(1/2)πR² - (3/2)πRh =
(1/2)πR(R - 3h)
h.
(4/9)a² - b² =
(2a/3 - b)(2a/3 + b)
i.
25x² - (t - 25)² =
(5x - (t - 25))(5x + (t - 25))
j.
(a + b - c)² - (a - b + c)² =
((a + b - c) - (a - b + c))((a + b - c) + (a - b + c)) =
(a + b - c - a + b - c)(a + b - c + a - b + c) =
(2b - 2c)(2a) =
4a(b - c)
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a.
33x³y⁴ - 22x²y² + 11x²y =
11x²y(3xy³ - 2y + 1) =
11x²y(1 + y(3xy² - 2))
b.
y(2x - 3) + 4(2x - 3) =
(2x - 3)(y + 4)
c.
4x³y⁴ - 17y⁴ + 35x¹²y⁷ =
y⁴(4x³ - 17 + 35x¹²y³) =
y⁴(x³(4 + 35x⁹y³) - 17)
d.
(x² + 2x²) - 9 =
3x² - 9 =
3(x² - 3) =
e. f.
(x - y)² -2(x - y) - 8 =
(x - y + 2)(x - y - 4)
g.
(1/2)πR² - (3/2)πRh =
(1/2)πR(R - 3h)
h.
(4/9)a² - b² =
(2a/3 - b)(2a/3 + b)
i.
25x² - (t - 25)² =
(5x - (t - 25))(5x + (t - 25))
j.
(a + b - c)² - (a - b + c)² =
((a + b - c) - (a - b + c))((a + b - c) + (a - b + c)) =
(a + b - c - a + b - c)(a + b - c + a - b + c) =
(2b - 2c)(2a) =
4a(b - c)