What is expand (λ-1/2)^2(λ-29/2) ?

The solution to expand (λ-1/2)^2(λ-29/2) is ((4λ^2-4λ+1)λ)/4-(29(4λ^2-4λ+1))/8

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expand (λ-1/2)^2(λ-29/2)

expand

(λ - \frac{1}{2})^{2} (λ - \frac{29}{2})

\frac{( 4 λ ^{2} - 4 λ + 1 ) λ}{4} - \frac{29 ( 4 λ ^{2} - 4 λ + 1 )}{8}

Solution steps

(λ - \frac{1}{2})^{2} (λ - \frac{29}{2})

Expand

(λ - \frac{1}{2})^{2} : \frac{4 λ ^{2} - 4 λ + 1}{4}

= \frac{4 λ ^{2} - 4 λ + 1}{4} (λ - \frac{29}{2})

Apply the distributive law:

a (b - c) = ab - a c

\frac{4 λ ^{2} - 4 λ + 1}{4} (λ - \frac{29}{2}) = \frac{4 λ ^{2} - 4 λ + 1}{4} λ - \frac{4 λ ^{2} - 4 λ + 1}{4} \cdot \frac{29}{2}

= \frac{4 λ ^{2} - 4 λ + 1}{4} λ - \frac{4 λ ^{2} - 4 λ + 1}{4} \cdot \frac{29}{2}

Simplify

\frac{4 λ ^{2} - 4 λ + 1}{4} λ - \frac{4 λ ^{2} - 4 λ + 1}{4} \cdot \frac{29}{2} : \frac{( 4 λ ^{2} - 4 λ + 1 ) λ}{4} - \frac{29 ( 4 λ ^{2} - 4 λ + 1 )}{8}

= \frac{( 4 λ ^{2} - 4 λ + 1 ) λ}{4} - \frac{29 ( 4 λ ^{2} - 4 λ + 1 )}{8}

\frac{15 x ^{2} - x + 2}{( x - 5 ) ( 3 x ^{2} + 4 x - 2 )}

a (- 1, 4) b (4, 6) c (2, - 2)

\frac{( s ^{2} + 1 )}{s ( s ^{2} + 1 + s )}

5 (3 x + y)^{2}

- \frac{1}{s ( s ^{2} + 1 )}

What is expand (λ-1/2)^2(λ-29/2) ?
The solution to expand (λ-1/2)^2(λ-29/2) is ((4λ^2-4λ+1)λ)/4-(29(4λ^2-4λ+1))/8