1. The problem is to factor each polynomial expression by finding the greatest common factor (GCF) and simplifying. 2. The formula for factoring by GCF is: $$a \cdot b + a \cdot c = a(b + c)$$ where $a$ is the GCF. 3. We apply this to each expression: - $-6(7x - 1) = -42x + 6$ - $9(4x^2 - 6x + 3) = 36x^2 - 54x + 27$ - $10 y^3 (7xy^3 - 8) = 70 x y^6 - 80 y^3$ - $-4x(9y^3 - 2xy - 1) = -36 x y^3 + 8 x^2 y + 4 x$ - $8x(3x^4 + 4x^2 + 4) = 24 x^5 + 32 x^3 + 32 x$ - $x(x^2 - 2x + 2) = x^3 - 2 x^2 + 2 x$ - $2 y^2 (9xy^3 - 2x + 7y) = 18 x y^5 - 4 x y^2 + 14 y^3$ - $9x^6 (x + 3) = 9 x^7 + 27 x^6$ - $-4(2xy^3 + 2x - 5) = -8 x y^3 - 8 x + 20$ - $-3(x^2 - x - 1) = -3 x^2 + 3 x + 3$ - $-6x^2 (10x^2 y - 8x^2 - 5y) = -60 x^4 y + 48 x^4 + 30 x^2 y$ - $-8x^2 (3x + 1) = -24 x^3 - 8 x^2$ - $-10(2x^4 y^6 + 2x + 1) = -20 x^4 y^6 - 20 x - 10$ - $7x(9y^2 + 10x^2) = 63 x y^2 + 70 x^3$ - $2 y^3 (3x - 4) = 6 x y^3 - 8 y^3$ - $-3xy(x - 3) = -3 x^2 y + 9 x y$ - $-9x(8x + 3) = -72 x^2 - 27 x$ - $10x(y - 1) = 10 x y - 10 x$ - $8x(9x^2 + 5x + 4) = 72 x^3 + 40 x^2 + 32 x$ - $3x(7x + 6) = 21 x^2 + 18 x$ 4. Each expression is factored by distributing the GCF and simplifying. Final answers are the expanded forms shown above.