What is expand (x-(-1/2))(x-(-2))(x-4)(x-6) ?

The solution to expand (x-(-1/2))(x-(-2))(x-4)(x-6) is x^4-(15x^3)/2+50x+24

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expand (x-(-1/2))(x-(-2))(x-4)(x-6)

expand

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

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

Solution steps

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

Simplify

(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)

Distribute parentheses

= 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

Simplify

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

7 (10 - 5)

(f - g) (2 π)

- \frac{6 ( - 3 x ^{2} + 1 )}{( 3 x ^{2} + 1 ) ^{2}}

\frac{- 3 x ^{2} + 8 x + 3}{( x ^{2} + 1 ) ^{2}}

(x + 4) (x + 2)

What is expand (x-(-1/2))(x-(-2))(x-4)(x-6) ?
The solution to expand (x-(-1/2))(x-(-2))(x-4)(x-6) is x^4-(15x^3)/2+50x+24