First, we can simplify the expression (x-5)/(4x+8) by factoring out 4 from both the numerator and denominator:
(x-5)/(4x+8) = (x-5)/4(x+2)
Then, we can use the distributive property to multiply this simplified expression by 12x^2+32x+16:
(x-5)/4(x+2) * (12x^2+32x+16)
= (x-5)*12x^2/4(x+2) + (x-5)*32x/4(x+2) + (x-5)*16/4(x+2)
= 3x^2(x-5)/(x+2) + 8x(x-5)/(x+2) + 4(x-5)/(x+2)
= (3x^3 - 7x^2 - 20x + 40)/(x+2)
Therefore, the final answer is (3x^3 - 7x^2 - 20x + 40)/(x+2).
(x-5)/(4x+8)*(12x^(2)+32x+16)
multiply
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can you multiply the expression?
Yes, I can multiply the expression (x-5)/(4x+8)*(12x^(2)+32x+16).
First, we can simplify the fraction (x-5)/(4x+8) to (x-5)/4(x+2).
Then, we can expand the expression 12x^2+32x+16 by factoring out 4 from each term:
12x^2 + 32x + 16 = 4(3x^2 + 8x + 4)
Now, we can substitute these expressions into the original equation and simplify using distributive property:
(x-5)/4(x+2) * 4(3x^2 + 8x + 4) = (x-5)(3x^2 + 8x + 4)/(x+2)
Finally, we can simplify this expression by expanding the numerator using distributive property and combining like terms:
(x-5)(3x^2 + 8x + 4)/(x+2) = 3x^3 - 7x^2 - 20x + 40 /(x+2)
Therefore, the simplified product of the original expression is 3x^3 - 7x^2 - 20x + 40 /(x+2).
First, we can simplify the fraction (x-5)/(4x+8) to (x-5)/4(x+2).
Then, we can expand the expression 12x^2+32x+16 by factoring out 4 from each term:
12x^2 + 32x + 16 = 4(3x^2 + 8x + 4)
Now, we can substitute these expressions into the original equation and simplify using distributive property:
(x-5)/4(x+2) * 4(3x^2 + 8x + 4) = (x-5)(3x^2 + 8x + 4)/(x+2)
Finally, we can simplify this expression by expanding the numerator using distributive property and combining like terms:
(x-5)(3x^2 + 8x + 4)/(x+2) = 3x^3 - 7x^2 - 20x + 40 /(x+2)
Therefore, the simplified product of the original expression is 3x^3 - 7x^2 - 20x + 40 /(x+2).
AAAaannndd the bot gets it wrong yet again!
(x-5)/(4x+8) * (12x^2+32x+16)
= (x-5)/(x+2) * (3x^2+8x+4)
= (x-5)/(x+2) * (3x+2)(x+2)
= (x-5)(3x+2)
= 3x^2-13x-10
(x-5)/(4x+8) * (12x^2+32x+16)
= (x-5)/(x+2) * (3x^2+8x+4)
= (x-5)/(x+2) * (3x+2)(x+2)
= (x-5)(3x+2)
= 3x^2-13x-10
I apologize for my mistake in the previous response. You are correct that after simplifying the fraction and factoring the quadratic expression, we can simplify and combine terms to get 3x^2 - 13x - 10. Thank you for pointing out the error, and I will be sure to double-check my work in the future.