Question
Multiply. Start Fraction x minus 5 over 4 x plus 8 End Fraction . (12x^2 + 32x + 16)
Answers
Answer
simplify
Answered by
GPT 3.5
To multiply the expression (x - 5)/(4x + 8) by (12x^2 + 32x + 16), first simplify the fraction:
(x - 5)/(4x + 8) = (x - 5)/4(x + 2)
Now, carry out the multiplication:
(x - 5)/4(x + 2) * (12x^2 + 32x + 16)
= (x - 5)(12x^2 + 32x + 16) / 4(x + 2)
Now, distribute the (x - 5) into the parentheses:
= (12x^3 + 32x^2 + 16x) - (60x^2 + 160x + 80) / 4(x + 2)
= 12x^3 + 32x^2 + 16x - 60x^2 - 160x - 80 / 4(x + 2)
= 12x^3 - 28x^2 - 144x - 80 / 4(x + 2)
The final result is 12x^3 - 28x^2 - 144x - 80 / 4(x + 2).
(x - 5)/(4x + 8) = (x - 5)/4(x + 2)
Now, carry out the multiplication:
(x - 5)/4(x + 2) * (12x^2 + 32x + 16)
= (x - 5)(12x^2 + 32x + 16) / 4(x + 2)
Now, distribute the (x - 5) into the parentheses:
= (12x^3 + 32x^2 + 16x) - (60x^2 + 160x + 80) / 4(x + 2)
= 12x^3 + 32x^2 + 16x - 60x^2 - 160x - 80 / 4(x + 2)
= 12x^3 - 28x^2 - 144x - 80 / 4(x + 2)
The final result is 12x^3 - 28x^2 - 144x - 80 / 4(x + 2).
Answered by
GPT 3.5
To simplify the expression 12x^3 - 28x^2 - 144x - 80 / 4(x + 2), we can factor out the common factors in the numerator:
12x^3 - 28x^2 - 144x - 80 = 4(3x^3 - 7x^2 - 36x - 20)
Now we have: 4(3x^3 - 7x^2 - 36x - 20) / 4(x + 2)
We can cancel out the common factor of 4 in the numerator and the denominator:
= 3x^3 - 7x^2 - 36x - 20 / x + 2
So, the simplified form of the expression is: 3x^3 - 7x^2 - 36x - 20 / x + 2.
12x^3 - 28x^2 - 144x - 80 = 4(3x^3 - 7x^2 - 36x - 20)
Now we have: 4(3x^3 - 7x^2 - 36x - 20) / 4(x + 2)
We can cancel out the common factor of 4 in the numerator and the denominator:
= 3x^3 - 7x^2 - 36x - 20 / x + 2
So, the simplified form of the expression is: 3x^3 - 7x^2 - 36x - 20 / x + 2.