\( \begin{array}{ll}\text { 1) } a^{1}-a^{2} b & \text { 1) } 5 x^{3} y^{3}-20 x y^{2} \\ \text { m) } 3 x^{2}-6 x^{3}+9 x^{4} & \text { n) } 4 p q^{2}-8 p q-12 p^{2} q \\ \text { a) } 5 a^{2}-10 a b+5 b^{2} & \text { p) } 3 a^{2}-6 a+9 \\ \text { q) }-6 a b^{1}+4 c b^{2}-2 d b & \text { r) } 7 x^{2} y^{2}-35 x y^{2} z-28 y \\ \text { s) } 16 a^{4} b^{8}-8 a^{3} b^{7}+36 a^{2} b^{3} & \text { t) } 4 \pi R^{2}-8 \pi R \\ \text { u) } \frac{1}{4} a^{2} b^{3}-\frac{1}{16} a^{3} b^{2} & \text { v) } 9 x^{3} y z^{2}+3 x y z-18 x\end{array} \)

Factor the expression by following steps: - step0: Factor: \(3x^{2}-6x^{3}+9x^{4}\) - step1: Factor the expression: \(3\left(x^{2}-2x^{3}+3x^{4}\right)\) - step2: Factor the expression: \(3x^{2}\left(1-2x+3x^{2}\right)\) Factor the expression \( 5 a^{2}-10 a b+5 b^{2 \). Factor the expression by following steps: - step0: Factor: \(5a^{2}-10ab+5b^{2}\) - step1: Factor the expression: \(5\left(a-b\right)^{2}\) Factor the expression \( a^{1}-a^{2} b \). Factor the expression by following steps: - step0: Factor: \(a-a^{2}b\) - step1: Factor the expression: \(a\left(1-ab\right)\) Factor the expression \( 3 a^{2}-6 a+9 \). Factor the expression by following steps: - step0: Factor: \(3a^{2}-6a+9\) - step1: Factor the expression: \(3\left(a^{2}-2a+3\right)\) Factor the expression \( 4 p q^{2}-8 p q-12 p^{2} q \). Factor the expression by following steps: - step0: Factor: \(4pq^{2}-8pq-12p^{2}q\) - step1: Factor the expression: \(4\left(pq^{2}-2pq-3p^{2}q\right)\) - step2: Factor the expression: \(4pq\left(q-2-3p\right)\) Factor the expression \( 5 x^{3} y^{3}-20 x y^{2} \). Factor the expression by following steps: - step0: Factor: \(5x^{3}y^{3}-20xy^{2}\) - step1: Factor the expression: \(5\left(x^{3}y^{3}-4xy^{2}\right)\) - step2: Factor the expression: \(5xy^{2}\left(x^{2}y-4\right)\) Factor the expression \( -6 a b^{1}+4 c b^{2}-2 d b \). Factor the expression by following steps: - step0: Factor: \(-6ab+4cb^{2}-2db\) - step1: Factor the expression: \(-2\left(3ba-2b^{2}c+bd\right)\) - step2: Factor the expression: \(-2b\left(3a-2cb+d\right)\) Factor the expression \( 9 x^{3} y z^{2}+3 x y z-18 x \). Factor the expression by following steps: - step0: Factor: \(9x^{3}yz^{2}+3xyz-18x\) - step1: Factor the expression: \(3\left(3x^{3}yz^{2}+xyz-6x\right)\) - step2: Factor the expression: \(3x\left(3x^{2}yz^{2}+yz-6\right)\) Factor the expression \( 4 \pi R^{2}-8 \pi R \). Factor the expression by following steps: - step0: Factor: \(4\pi R^{2}-8\pi R\) - step1: Factor the expression: \(4\pi \left(R^{2}-2R\right)\) - step2: Factor the expression: \(4\pi R\left(R-2\right)\) Factor the expression \( 16 a^{4} b^{8}-8 a^{3} b^{7}+36 a^{2} b^{3 \). Factor the expression by following steps: - step0: Factor: \(16a^{4}b^{8}-8a^{3}b^{7}+36a^{2}b^{3}\) - step1: Factor the expression: \(4\left(4a^{4}b^{8}-2a^{3}b^{7}+9a^{2}b^{3}\right)\) - step2: Factor the expression: \(4a^{2}b^{3}\left(4a^{2}b^{5}-2ab^{4}+9\right)\) Factor the expression \( 7 x^{2} y^{2}-35 x y^{2} z-28 y \). Factor the expression by following steps: - step0: Factor: \(7x^{2}y^{2}-35xy^{2}z-28y\) - step1: Factor the expression: \(7\left(y^{2}x^{2}-5y^{2}xz-4y\right)\) - step2: Factor the expression: \(7y\left(x^{2}y-5xyz-4\right)\) Factor the expression \( \frac{1}{4} a^{2} b^{3}-\frac{1}{16} a^{3} b^{2 \). Factor the expression by following steps: - step0: Factor: \(\frac{1}{4}a^{2}b^{3}-\frac{1}{16}a^{3}b^{2}\) - step1: Factor the expression: \(\frac{1}{16}\left(4a^{2}b^{3}-a^{3}b^{2}\right)\) - step2: Factor the expression: \(\frac{1}{16}a^{2}b^{2}\left(4b-a\right)\) Here are the factored forms of the given expressions: 1) \( a^{1}-a^{2} b \) **Factored Form:** \( a(1-ab) \) 2) \( 5 x^{3} y^{3}-20 x y^{2} \) **Factored Form:** \( 5xy^{2}(x^{2}y-4) \) 3) \( 3 x^{2}-6 x^{3}+9 x^{4} \) **Factored Form:** \( 3x^{2}(1-2x+3x^{2}) \) 4) \( 4 p q^{2}-8 p q-12 p^{2} q \) **Factored Form:** \( 4pq(q-2-3p) \) 5) \( 5 a^{2}-10 a b+5 b^{2} \) **Factored Form:** \( 5(a-b)^{2} \) 6) \( 3 a^{2}-6 a+9 \) **Factored Form:** \( 3(a^{2}-2a+3) \) 7) \( -6 a b^{1}+4 c b^{2}-2 d b \) **Factored Form:** \( -2b(3a-2cb+d) \) 8) \( 7 x^{2} y^{2}-35 x y^{2} z-28 y \) **Factored Form:** \( 7y(x^{2}y-5xyz-4) \) 9) \( 16 a^{4} b^{8}-8 a^{3} b^{7}+36 a^{2} b^{3} \) **Factored Form:** \( 4a^{2}b^{3}(4a^{2}b^{5}-2ab^{4}+9) \) 10) \( 4 \pi R^{2}-8 \pi R \) **Factored Form:** \( 4\pi R(R-2) \) 11) \( \frac{1}{4} a^{2} b^{3}-\frac{1}{16} a^{3} b^{2} \) **Factored Form:** \( \frac{1}{16}a^{2}b^{2}(4b-a) \) 12) \( 9 x^{3} y z^{2}+3 x y z-18 x \) **Factored Form:** \( 3x(3x^{2}yz^{2}+yz-6) \) These factorizations simplify the expressions and reveal their underlying structure. If you need further assistance or explanations on any specific factorization, feel free to ask!