展开 xz(x+3y+5z)^2

解答

展开

x z (x + 3 y + 5 z)^{2}

10 x^{2} z^{2} + 6 x^{2} zy + x^{3} z + 25 x z^{3} + 9 x z y^{2} + 30 x z^{2} y

求解步骤

x z (x + 3 y + 5 z)^{2}

(x + 3 y + 5 z)^{2} = 10 x z + 6 x y + x^{2} + 25 z^{2} + 9 y^{2} + 30 zy

= x z (x^{2} + 10 x z + 6 x y + 25 z^{2} + 30 zy + 9 y^{2})

打开括号

= x z \cdot 10 x z + x z \cdot 6 x y + x z x^{2} + x z \cdot 25 z^{2} + x z \cdot 9 y^{2} + x z \cdot 30 zy

= 10 xx zz + 6 xx zy + x^{2} x z + 25 x z^{2} z + 9 x z y^{2} + 30 x zzy

化简

10 xx zz + 6 xx zy + x^{2} x z + 25 x z^{2} z + 9 x z y^{2} + 30 x zzy : 10 x^{2} z^{2} + 6 x^{2} zy + x^{3} z + 25 x z^{3} + 9 x z y^{2} + 30 x z^{2} y

= 10 x^{2} z^{2} + 6 x^{2} zy + x^{3} z + 25 x z^{3} + 9 x z y^{2} + 30 x z^{2} y

s im pl i f y (5 x + 8 \circ x^{2} + x) (x)

e x p an d (2, - 1) y (- 1, \frac{9}{- 7})

e x p an d \frac{7 ( - 4.9 x ^{2} + 250 )}{7 x - 50}

e x p an d (2 x + 3)^{2} - 3 (2 x + 3) +!

e x p an d \frac{( x - yz ) ^{2}}{4}