対称式の公式まとめ

覚えた方がいい、展開公式と 対称式の公式をまとめます・・・

$$(a + b)^2 = a^2 + 2ab + b^2$$ $$(a - b)^2 = a^2 - 2ab + b^2$$

$$(a + b)(a - b) = a^2 - b^2$$

$$(x + a)(x + b) = x^2 + (a + b)x + ab$$ $$(ax + b)(cx + d) = acx^2 + (ad + bc)x + bd$$

$$(a + b)(a^2 - ab + b^2) = a^3 + b^3$$ $$(a - b)(a^2 + ab + b^2) = a^3 - b^3$$

$$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$$ $$(a - b)^3 = a^3 + -3a^2b + 3ab^2 - b^3$$

$$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac$$ $$(a + b + c)(a^2 + b^2 + c^2 -ab - bc -ca) = a^3 + b^3 + c^3 -3abc$$

$$x^2 + y^2 + z^2 = (x + y + z)^2 -2(xy + yz + zx)$$ $$x^3 + y^3 + z^3 = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx) + 3xyz$$ $$x^4 + y^4 + z^4 = (x^2 + y^2 + z^2)^2 -2(x^2y^2 + y^2z^2 + z^2x^2)$$

2018/5/4