(x-5)/(4x+8)*(12x^(2)+32x+16)
multiply
can you multiply the expression?
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
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.
To multiply the given expression, we need to apply the distributive property of multiplication over addition. This property states that we must multiply each term in the first expression by each term in the second expression.
The given expression is:
(x-5)/(4x+8) * (12x^(2) + 32x + 16)
To multiply, we will follow these steps:
Step 1: Distribute the numerator of the first fraction (x-5) to the three terms in the second expression (12x^(2), 32x, and 16).
Step 2: Distribute the denominator of the first fraction (4x+8) to the three terms in the second expression (12x^(2), 32x, and 16).
Step 3: Simplify both the numerator and denominator, if possible.
Let's multiply the expression step by step:
Step 1:
(x-5) * 12x^(2) = 12x^(3) - 60x^(2) [Multiply each term in the first expression by the first term in the second expression.]
(x-5) * 32x = 32x^(2) - 160x [Multiply each term in the first expression by the second term in the second expression.]
(x-5) * 16 = 16x - 80 [Multiply each term in the first expression by the third term in the second expression.]
Step 2:
(4x+8) * 12x^(2) = 48x^(3) + 96x^(2) [Multiply each term in the second expression by the first term in the second fraction.]
(4x+8) * 32x = 128x^(2) + 256x [Multiply each term in the second expression by the second term in the second fraction.]
(4x+8) * 16 = 64x + 128 [Multiply each term in the second expression by the third term in the second fraction.]
Step 3:
Now, we can combine like terms from the numerator and denominator:
Numerator = (12x^(3) - 60x^(2)) + (32x^(2) - 160x) + (16x - 80)
= 12x^(3) - 28x^(2) - 144x - 80
Denominator = (48x^(3) + 96x^(2)) + (128x^(2) + 256x) + (64x + 128)
= 48x^(3) + 224x^(2) + 320x + 128
Therefore, the multiplication of the given expression is:
(12x^(3) - 28x^(2) - 144x - 80) / (48x^(3) + 224x^(2) + 320x + 128)
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).
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).