因式分解 4x^2-36xy+81y^2

解答

因式分解

4 x^{2} - 36 x y + 81 y^{2}

(2 x - 9 y)^{2}

求解步骤

4 x^{2} - 36 x y + 81 y^{2}

改写为形式

a^{2} + 2 ab + b^{2} :

4 x^{2} = (2 x)^{2}

81 y^{2} = (9 y)^{2}

- 36 x y = - 2 \cdot 2 x \cdot 9 y

= (2 x)^{2} - 2 \cdot 2 x \cdot 9 y + (9 y)^{2}

使用完全平方公式:

a^{2} - 2 ab + b^{2} = (a - b)^{2}

(2 x)^{2} - 2 \cdot 2 x \cdot 9 y + (9 y)^{2} = (2 x - 9 y)^{2}

= (2 x - 9 y)^{2}

s im pl i f y \frac{15 x ^{6} y}{25 x ^{2} y ^{4}}

s im pl i f y \frac{4 j ^{7}}{5 ( j ^{2} ) ^{3}}

x^{2} \leq 3 - 2 x

f a c t or x^{3} y^{3} + 2 x^{3} + 5 x^{2} y^{3} + 10 x^{2}

x^{2} - 2 x = 8