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Show that: (3x-1)(x+5)(4x-3) = 12x^3 + 47x^2 - 62x +15 for all values of x. (3x-1)(x+5)(4x-3) = (?????)(4x-3) Expand into 6 terms: ???????? Simplify: ???????? Thank you.

Verified Answer :

MissPhiladelphia

(3x - 1)( x + 5)(4x - 3) = 12x^3 + 47x^2 - 62x +15 

(3x^2 –
x + 15x - 5)( 4x – 3 ) = 12x^3 + 47x^2 - 62x +15 

(3x^2 +
14x - 5)( 4x – 3 ) = 12x^3 + 47x^2 - 62x +15 

12x^3 –
9x^2 + 56x^2 – 42x – 20x + 15 = 12x^3 +
47x^2 - 62x +15 

12x^3 –
47x^2 - 62x + 15 = 12x^3 + 47x^2 - 62x +15 

 

Answer with Step-by-step explanation:

We have to show that:

\((3x-1)(x+5)(4x-3) = 12x^3 + 47x^2 - 62x +15\)

\((3x-1)(x+5)(4x-3) = (3x(x+5)-1(x+5))(4x-3)\\\\=(3x^2+15x-x-5)(4x-3)\\\\=(3x^2+14x-5)(4x-3)\\\\=3x^2(4x-3)+14x(4x-3)-5(4x-3)\\\\=12x^3-9x^2+56x^2-42x-20x+15\\\\=12x^3+47x^2-62x+15\)

Hence, we have

\((3x-1)(x+5)(4x-3) = 12x^3 + 47x^2 - 62x +15\)