Question

Please I need help and I’m stumped here.

Answer 1

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:

$a^{mn} = (a^m)^{n}\\\\a^{m}*a^{n}= a^{m+n}$

$\sqrt[4]{144x^{12}y^{7}} =\sqrt[4]{2*2*2*2*3*3*x^{3*4}*y^{4+3}} \\\\=\sqrt[4]{2^{4}*9*(x^{3})^{4}*y^{4}*y^{3}}\\\\=2*x^{3}*y\sqrt[4]{9y^{3}}\\\\ =2x^{3}y\sqrt[4]{9y^{3}}$

4)

$\sqrt[3]{\frac{320a^{10}}{27b^{6}}}= \sqrt[3]{\frac{8*8*5a^{3+3+3+1}}{3*3*3b^{3+3}}}\\\\=\sqrt[3]{\frac{2^{3}*2^{3}*5a^{3}*a^{3}*a^{3}*a}{3^{3}b^{3}*b^{3}}}\\\\=\frac{2*2*a*a*a}{3b*b}\sqrt[3]{\frac{5a}{1}}\\\\=\frac{4a^{2}}{3b^{2}}\sqrt[3]{5a}$

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)