Answer:
Step-by-step explanation:
1) For complex numbers addition, add the real parts and imaginary party separately.
(2 +5i) - (-6 + 3i) = 2 + 5i + 6 - 3i
= 2+ 6 + 5i - 3i
= 8 + 2i
2)Use FOIL method
(-4 +2i)(3 - 7i) = -4*3 + (-4)*(-7i) + 2i* 3 + (2i)*(-7i)
= -12 + 28i + 6i -14i² {i² = -1}
= -12 + 28i + 6i - 14*(-1)
= -12 + 28i + 6i + 14 {Combine like terms}
= -12 + 14 + 28i + 6i
= - 2 + 34i
3)Hint:
![a^{mn} = (a^m)^{n}\\\\a^{m}*a^{n}= a^{m+n}](https://tex.z-dn.net/?f=a%5E%7Bmn%7D%20%3D%20%28a%5Em%29%5E%7Bn%7D%5C%5C%5C%5Ca%5E%7Bm%7D%2Aa%5E%7Bn%7D%3D%20a%5E%7Bm%2Bn%7D)
![\sqrt[4]{144x^{12}y^{7}} =\sqrt[4]{2*2*2*2*3*3*x^{3*4}*y^{4+3}} \\\\=\sqrt[4]{2^{4}*9*(x^{3})^{4}*y^{4}*y^{3}}\\\\=2*x^{3}*y\sqrt[4]{9y^{3}}\\\\ =2x^{3}y\sqrt[4]{9y^{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B144x%5E%7B12%7Dy%5E%7B7%7D%7D%20%3D%5Csqrt%5B4%5D%7B2%2A2%2A2%2A2%2A3%2A3%2Ax%5E%7B3%2A4%7D%2Ay%5E%7B4%2B3%7D%7D%20%20%5C%5C%5C%5C%3D%5Csqrt%5B4%5D%7B2%5E%7B4%7D%2A9%2A%28x%5E%7B3%7D%29%5E%7B4%7D%2Ay%5E%7B4%7D%2Ay%5E%7B3%7D%7D%5C%5C%5C%5C%3D2%2Ax%5E%7B3%7D%2Ay%5Csqrt%5B4%5D%7B9y%5E%7B3%7D%7D%5C%5C%5C%5C%20%3D2x%5E%7B3%7Dy%5Csqrt%5B4%5D%7B9y%5E%7B3%7D%7D)
4)
![\sqrt[3]{\frac{320a^{10}}{27b^{6}}}= \sqrt[3]{\frac{8*8*5a^{3+3+3+1}}{3*3*3b^{3+3}}}\\\\=\sqrt[3]{\frac{2^{3}*2^{3}*5a^{3}*a^{3}*a^{3}*a}{3^{3}b^{3}*b^{3}}}\\\\=\frac{2*2*a*a*a}{3b*b}\sqrt[3]{\frac{5a}{1}}\\\\=\frac{4a^{2}}{3b^{2}}\sqrt[3]{5a}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B320a%5E%7B10%7D%7D%7B27b%5E%7B6%7D%7D%7D%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B8%2A8%2A5a%5E%7B3%2B3%2B3%2B1%7D%7D%7B3%2A3%2A3b%5E%7B3%2B3%7D%7D%7D%5C%5C%5C%5C%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B2%5E%7B3%7D%2A2%5E%7B3%7D%2A5a%5E%7B3%7D%2Aa%5E%7B3%7D%2Aa%5E%7B3%7D%2Aa%7D%7B3%5E%7B3%7Db%5E%7B3%7D%2Ab%5E%7B3%7D%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B2%2A2%2Aa%2Aa%2Aa%7D%7B3b%2Ab%7D%5Csqrt%5B3%5D%7B%5Cfrac%7B5a%7D%7B1%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B4a%5E%7B2%7D%7D%7B3b%5E%7B2%7D%7D%5Csqrt%5B3%5D%7B5a%7D)
5) 4x² + 28x + 49 = 4x² + 14x +14x + 7*7
= 2x(2x + 7) + 7(2x + 7)
=(2x+ 7)(2x + 7)
6) 2x² + 3x - 20 = 2x² +8x - 5x - 5 *4
=2x(x + 4) - 5(x + 4)
= (x + 4)(2x - 5)