Question

Express the product of (1/2x - 5/3) and (1/2x-1) as a trinomial in simplest form.

Answer 1

`\longrightarrow{\green{ \frac{ {x}^(2) }{4} - (4x)/(3) + (5)/(3) }}`

`\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}`

`( (1)/(2) x - (5)/(3) ) * ( (1)/(2) x - 1) \\ \\ = (1)/(2) x \: ( (1)/(2) x - 1) - (5)/(3) \: ( (1)/(2) x - 1) \\ \\ = \frac{ {x}^(2) }{4} - (x)/(2) - (5x)/(6) + (5)/(3) \\ \\ = \frac{ {x}^(2) * 3 }{4 * 3} - (x * 6)/(2 * 6) - (5x * 2)/(6 * 2) + (5 * 4)/(3 * 4) \\\\ = \frac{3 {x}^(2) - 6x - 10x + 20}{12} \\ \\ = \frac{3 {x}^(2) - 16x + 20 }{12} \\\\= \frac{ {x}^(2) }{4} - (4x)/(3) + (5)/(3)`

`\bold{ \green{ \star{ \orange{Mystique35}}}}⋆`

Answer 2

Can be simplified to
1/4x^2 -4/3x +5/3
Using the FOIL method