Escreve na forma reduzida
Monómios e polinómios: Matematicamente Falando 8 - Pág. 133 Ex. 5
Enunciado
Escreve na forma reduzida.
| a) | \(3 \times 5x\) |
| b) | \(2a \times \left( { – a} \right)\) |
| c) | \( – 3yz \times \frac{1}{3}y\) |
| d) | \( – 2{x^2} \times \left( { – 5{x^3}} \right)\) |
| e) | \(3{a^2}b \times \frac{{ab}}{3}\) |
| f) | \({\left( {{x^2}y} \right)^2}\) |
| g) | \({\left( { – \frac{1}{2}m{n^2}p} \right)^3}\) |
| h) | \(2x\left( {{x^2} + 3x – \frac{1}{2}} \right)\) |
| i) | \( – 3x\left( { – x + 4} \right)\) |
| j) | \(\left( {{x^2} – 7x} \right) \times \frac{{{x^3}}}{2}\) |
| k) | \(\left( {n – 2} \right)\left( {n + 3} \right)\) |
| l) | \(\left( {3a – 1} \right)\left( {{a^2} + \frac{1}{4}} \right)\) |
| m) | \(\left( {1 – m – {m^2}} \right)\left( {m + 2} \right)\) |
| n) | \(\left( {\frac{a}{2} – 3} \right)\left( {{a^2} – 6a} \right)\) |
Resolução
Escrevendo na forma reduzida, temos:
| a) | \(3 \times 5x = 15x\) |
| b) | \(2a \times \left( { – a} \right) = – 2{a^2}\) |
| c) | \( – 3yz \times \frac{1}{3}y = – {y^2}z\) |
| d) | \( – 2{x^2} \times \left( { – 5{x^3}} \right) = \left( { – 2 \times \left( { – 5} \right)} \right) \times \left( {{x^2} \times {x^3}} \right) = 10{x^5}\) |
| e) | \(3{a^2}b \times \frac{{ab}}{3} = {a^3}{b^2}\) |
| f) | \({\left( {{x^2}y} \right)^2} = \left( {{x^2}y} \right) \times \left( {{x^2}y} \right) = \left( {{x^2} \times {x^2}} \right) \times \left( {y \times y} \right) = {x^4}{y^2}\) ou \({\left( {{x^2}y} \right)^2} = {\left( {{x^2}} \right)^2} \times {\left( y \right)^2} = {x^4}{y^2}\) |
| g) | \({\left( { – \frac{1}{2}m{n^2}p} \right)^3} = {\left( { – \frac{1}{2}} \right)^3} \times {\left( m \right)^3} \times {\left( {{n^2}} \right)^3} \times {\left( p \right)^3} = – \frac{1}{8}{m^3}{n^6}{p^3}\) |
| h) | \(2x\left( {{x^2} + 3x – \frac{1}{2}} \right) = 2{x^3} + 6{x^2} – x\) |
| i) | \( – 3x\left( { – x + 4} \right) = 3{x^2} – 12x\) |
| j) | \(\left( {{x^2} – 7x} \right) \times \frac{{{x^3}}}{2} = \frac{{{x^5}}}{2} – \frac{7}{2}{x^4}\) |
| k) | \(\left( {n – 2} \right)\left( {n + 3} \right) = {n^2} + 3n – 2n – 6 = {n^2} + n – 6\) |
| l) | \(\left( {3a – 1} \right)\left( {{a^2} + \frac{1}{4}} \right) = 3{a^3} + \frac{3}{4}a – {a^2} – \frac{1}{4} = 3{a^3} – {a^2} + \frac{3}{4}a – \frac{1}{4}\) |
| m) | \(\left( {1 – m – {m^2}} \right)\left( {m + 2} \right) = m + 2 – {m^2} – 2m – {m^3} – 2{m^2} = – {m^3} – 3{m^2} – m + 2\) |
| n) | \(\left( {\frac{a}{2} – 3} \right)\left( {{a^2} – 6a} \right) = \frac{{{a^3}}}{2} – 3{a^2} – 3{a^2} + 18a = \frac{{{a^3}}}{2} – 6{a^2} + 18a\) |
