第1章前提知識Prerequisites

Key Equations重要な式

Rules of Exponents For nonzero real numbers $a$ and $b$ and integers $m$ and $n$ 指数の規則　0でない実数 $a$ 、 $b$ と整数 $m$ 、 $n$ について
Product rule積の規則	$a^{m} \cdot a^{n} = a^{m + n}$
Quotient rule商の規則	$\frac{a^{m}}{a^{n}} = a^{m - n}$
Power rule累乗の規則	${(a^{m})}^{n} = a^{m \cdot n}$
Zero exponent rule0乗の規則	$a^{0} = 1$
Negative rule負の規則	$a^{- n} = \frac{1}{a^{n}}$
Power of a product rule積の累乗の規則	${(a \cdot b)}^{n} = a^{n} \cdot b^{n}$
Power of a quotient rule商の累乗の規則	${(\frac{a}{b})}^{n} = \frac{a^{n}}{b^{n}}$

perfect square trinomial完全平方の三項式	${(x + a)}^{2} = (x + a) (x + a) = x^{2} + 2 a x + a^{2}$
difference of squares平方の差	$(a + b) (a - b) = a^{2} - b^{2}$

difference of squares平方の差	$a^{2} - b^{2} = (a + b) (a - b)$
perfect square trinomial完全平方の三項式	$a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$
sum of cubes立方の和	$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$
difference of cubes立方の差	$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$