展开 (x-(-1/2))(x-(-2))(x-4)(x-6)

解答

展开

(x - (- \frac{1}{2})) (x - (- 2)) (x - 4) (x - 6)

x^{4} - \frac{15 x ^{3}}{2} + 50 x + 24

求解步骤

(x - (- \frac{1}{2})) (x - (- 2)) (x - 4) (x - 6)

化简

(x - (- \frac{1}{2})) (x - (- 2)) (x - 4) (x - 6) : (x + \frac{1}{2}) (x + 2) (x - 4) (x - 6)

= (x + \frac{1}{2}) (x + 2) (x - 4) (x - 6)

Apply FOIL method

(x + \frac{1}{2}) (x + 2) : x^{2} + \frac{5}{2} x + 1

= (x^{2} + \frac{5}{2} x + 1) (x - 4) (x - 6)

Apply FOIL method

(x - 4) (x - 6) : x^{2} - 10 x + 24

= (x^{2} + \frac{5}{2} x + 1) (x^{2} - 10 x + 24)

打开括号

= x^{2} x^{2} + x^{2} (- 10 x) + x^{2} \cdot 24 + \frac{5}{2} x x^{2} + \frac{5}{2} x (- 10 x) + \frac{5}{2} x \cdot 24 + 1 \cdot x^{2} + 1 \cdot (- 10 x) + 1 \cdot 24

化简

x^{2} x^{2} + x^{2} (- 10 x) + x^{2} \cdot 24 + \frac{5}{2} x x^{2} + \frac{5}{2} x (- 10 x) + \frac{5}{2} x \cdot 24 + 1 \cdot x^{2} + 1 \cdot (- 10 x) + 1 \cdot 24 : x^{4} - \frac{15 x ^{3}}{2} + 50 x + 24

= x^{4} - \frac{15 x ^{3}}{2} + 50 x + 24

e x p an d 7 (10 - 5)

e x p an d (f - g) (2 π)

e x p an d - \frac{6 ( - 3 x ^{2} + 1 )}{( 3 x ^{2} + 1 ) ^{2}}

e x p an d \frac{- 3 x ^{2} + 8 x + 3}{( x ^{2} + 1 ) ^{2}}

s im pl i f y (x + 4) (x + 2)