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Popular Álgebra >

expandir (7-y^2)^6

Solução

expandir

(7 - y^{2})^{6}

Solução

117649 - 100842 y^{2} + 36015 y^{4} - 6860 y^{6} + 735 y^{8} - 42 y^{10} + y^{12}

Passos da solução

(7 - y^{2})^{6}

Aplicar o teorema do binômio:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 7, b = - y^{2}

= i = 0 \sum 6 (i 6) \cdot 7^{(6 - i)} (- y^{2})^{i}

Expandir a soma

= \frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 7^{6} (- y^{2})^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 7^{5} (- y^{2})^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 7^{4} (- y^{2})^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 7^{3} (- y^{2})^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 7^{2} (- y^{2})^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 7^{1} (- y^{2})^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 7^{0} (- y^{2})^{6}

Simplificar

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 7^{6} (- y^{2})^{0} : 117649

Simplificar

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 7^{5} (- y^{2})^{1} : - 100842 y^{2}

Simplificar

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 7^{4} (- y^{2})^{2} : 36015 y^{4}

Simplificar

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 7^{3} (- y^{2})^{3} : - 6860 y^{6}

Simplificar

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 7^{2} (- y^{2})^{4} : 735 y^{8}

Simplificar

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 7^{1} (- y^{2})^{5} : - 42 y^{10}

Simplificar

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 7^{0} (- y^{2})^{6} : y^{12}

= 117649 - 100842 y^{2} + 36015 y^{4} - 6860 y^{6} + 735 y^{8} - 42 y^{10} + y^{12}

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