Answer: 21
12
Log8(8 is under the log) the answer is 7
Step-by-step explanation:
15
Step-by-step explanation:
The answer of this problem is the letter C. -3.3
The product is ![104 x^{4}+16 \sqrt{30} x^{4}](https://tex.z-dn.net/?f=104%20x%5E%7B4%7D%2B16%20%5Csqrt%7B30%7D%20x%5E%7B4%7D)
Explanation:
The given expression is ![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D)
We need to determine the product of the given expression.
First, we shall simplify the given expression.
Thus, we have,
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x \sqrt{5} x+2 x^{2} \sqrt{6}\right)^2](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D%5Cleft%284%20x%20%5Csqrt%7B5%7D%20x%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E2)
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)^2](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D%5Cleft%284%20x%5E%7B2%7D%20%5Csqrt%7B5%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E2)
Expanding the expression, we have,
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D%5Cleft%284%20x%5E%7B2%7D%20%5Csqrt%7B5%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5Cleft%284%20x%5E%7B2%7D%20%5Csqrt%7B5%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29)
Now, we shall apply FOIL, we get,
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}\right)^{2}+2 ( 2 x^{2} \sqrt{6})(4 x^{2} \sqrt{5})+\left(2 x^{2} \sqrt{6}\right)^{2}](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D%5Cleft%284%20x%5E%7B2%7D%20%5Csqrt%7B5%7D%5Cright%29%5E%7B2%7D%2B2%20%28%202%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%29%284%20x%5E%7B2%7D%20%5Csqrt%7B5%7D%29%2B%5Cleft%282%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D)
Simplifying the terms, we have,
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=16 \cdot 5 x^{4}+16 \sqrt{30} x^{4}+4 \cdot 6 x^{4}](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D16%20%5Ccdot%205%20x%5E%7B4%7D%2B16%20%5Csqrt%7B30%7D%20x%5E%7B4%7D%2B4%20%5Ccdot%206%20x%5E%7B4%7D)
Multiplying, we get,
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=80 x^{4}+16 \sqrt{30} x^{4}+24 x^{4}](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D80%20x%5E%7B4%7D%2B16%20%5Csqrt%7B30%7D%20x%5E%7B4%7D%2B24%20x%5E%7B4%7D)
Adding the like terms, we get,
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=104 x^{4}+16 \sqrt{30} x^{4}](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D104%20x%5E%7B4%7D%2B16%20%5Csqrt%7B30%7D%20x%5E%7B4%7D)
Thus, the product of the given expression is ![104 x^{4}+16 \sqrt{30} x^{4}](https://tex.z-dn.net/?f=104%20x%5E%7B4%7D%2B16%20%5Csqrt%7B30%7D%20x%5E%7B4%7D)