Scomponi i seguenti polinomi, eseguendo raccoglimenti totali di numerici). ans \( \frac{1}{2} x(x-1)+\frac{3}{2} x(x-1)^{2}+\frac{1}{4} x^{2}(x-1) \) and \( \frac{1}{3} t^{3}(t-1)^{2}+\frac{2}{3} t^{2}(t-1)^{4} \) \( =4510,5 p^{2}(p+q)^{2}-0,25 p(p+q)^{3} \) \( =45) 0,2 a^{5}(b+1)^{8}+5^{-2} a^{3}(b+1)^{6} \) \( =47 a^{x+2}(b-1)^{y}+a^{x+3}(b-1)^{y+1}+a^{x+4}(b-1)^{y} \) \( =48 x^{n+1}(y-1)^{n}-x^{n}(y-1)^{n+1}+x^{n}(y-1)^{n} \)

Factor the expression by following steps: - step0: Factor: \(4510.5p^{2}\left(p+q\right)^{2}-0.25p\left(p+q\right)^{3}\) - step1: Convert the expressions: \(\frac{9021}{2}p^{2}\left(p+q\right)^{2}-\frac{1}{4}p\left(p+q\right)^{3}\) - step2: Rewrite the expression: \(p\left(p+q\right)^{2}\times \frac{9021}{2}p-p\left(p+q\right)^{2}\times \frac{1}{4}\left(p+q\right)\) - step3: Factor the expression: \(p\left(p+q\right)^{2}\left(\frac{9021}{2}p-\frac{1}{4}\left(p+q\right)\right)\) - step4: Factor the expression: \(p\left(p+q\right)^{2}\times \frac{1}{4}\left(18041p-q\right)\) - step5: Calculate: \(\frac{1}{4}p\left(p+q\right)^{2}\left(18041p-q\right)\) Factor the expression \( 48 x^{n+1}(y-1)^{n}-x^{n}(y-1)^{n+1}+x^{n}(y-1)^{n} \). Factor the expression by following steps: - step0: Factor: \(48x^{n+1}\left(y-1\right)^{n}-x^{n}\left(y-1\right)^{n+1}+x^{n}\left(y-1\right)^{n}\) - step1: Calculate: \(48x^{n+1}\left(y-1\right)^{n}-x^{n}\left(y-1\right)^{n+1}+\left(x\left(y-1\right)\right)^{n}\) - step2: Factor the expression: \(\left(x\left(y-1\right)\right)^{n}\left(48x-\left(y-1\right)+1\right)\) Factor the expression \( \frac{1}{2} x(x-1)+\frac{3}{2} x(x-1)^{2}+\frac{1}{4} x^{2}(x-1) \). Factor the expression by following steps: - step0: Factor: \(\frac{1}{2}x\left(x-1\right)+\frac{3}{2}x\left(x-1\right)^{2}+\frac{1}{4}x^{2}\left(x-1\right)\) - step1: Factor the expression: \(\frac{1}{4}\left(2x\left(x-1\right)+6x\left(x-1\right)^{2}+\left(x-1\right)x^{2}\right)\) - step2: Factor the expression: \(\frac{1}{4}x\left(x-1\right)\left(2+6\left(x-1\right)+x\right)\) - step3: Calculate: \(\frac{1}{4}x\left(x-1\right)\left(-4+7x\right)\) Factor the expression \( 47 a^{x+2}(b-1)^{y}+a^{x+3}(b-1)^{y+1}+a^{x+4}(b-1)^{y} \). Factor the expression by following steps: - step0: Factor: \(47a^{x+2}\left(b-1\right)^{y}+a^{x+3}\left(b-1\right)^{y+1}+a^{x+4}\left(b-1\right)^{y}\) - step1: Factor the expression: \(a^{x+2}\left(b-1\right)^{y}\left(47+\left(b-1\right)a+a^{2}\right)\) Factor the expression \( \frac{1}{3} t^{3}(t-1)^{2}+\frac{2}{3} t^{2}(t-1)^{4} \). Factor the expression by following steps: - step0: Factor: \(\frac{1}{3}t^{3}\left(t-1\right)^{2}+\frac{2}{3}t^{2}\left(t-1\right)^{4}\) - step1: Rewrite the expression: \(t^{2}\left(t-1\right)^{2}\times \frac{1}{3}t+t^{2}\left(t-1\right)^{2}\times \frac{2}{3}\left(t-1\right)^{2}\) - step2: Factor the expression: \(t^{2}\left(t-1\right)^{2}\left(\frac{1}{3}t+\frac{2}{3}\left(t-1\right)^{2}\right)\) - step3: Factor the expression: \(t^{2}\left(t-1\right)^{2}\times \frac{1}{3}\left(-3t+2t^{2}+2\right)\) - step4: Calculate: \(\frac{1}{3}t^{2}\left(t-1\right)^{2}\left(-3t+2t^{2}+2\right)\) Ecco i risultati della scomposizione dei polinomi richiesti: 1. **Polinomio**: \( \frac{1}{2} x(x-1)+\frac{3}{2} x(x-1)^{2}+\frac{1}{4} x^{2}(x-1) \) **Scomposizione**: \[ \frac{1}{4}x(x-1)(-4+7x) \] 2. **Polinomio**: \( \frac{1}{3} t^{3}(t-1)^{2}+\frac{2}{3} t^{2}(t-1)^{4} \) **Scomposizione**: \[ \frac{1}{3}t^{2}(t-1)^{2}(-3t+2t^{2}+2) \] 3. **Polinomio**: \( 4510.5 p^{2}(p+q)^{2}-0.25 p(p+q)^{3} \) **Scomposizione**: \[ \frac{1}{4}p(p+q)^{2}(18041p-q) \] 4. **Polinomio**: \( 45 \cdot 0.2 a^{5}(b+1)^{8}+5^{-2} a^{3}(b+1)^{6} \) **Risultato**: Non è stato possibile trovare un risultato per questo polinomio. 5. **Polinomio**: \( 47 a^{x+2}(b-1)^{y}+a^{x+3}(b-1)^{y+1}+a^{x+4}(b-1)^{y} \) **Scomposizione**: \[ a^{x+2}(b-1)^{y}(47+(b-1)a+a^{2}) \] 6. **Polinomio**: \( 48 x^{n+1}(y-1)^{n}-x^{n}(y-1)^{n+1}+x^{n}(y-1)^{n} \) **Scomposizione**: \[ (x(y-1))^{n}(48x-(y-1)+1) \] Se hai bisogno di ulteriori chiarimenti o di assistenza con altri polinomi, fammi sapere!