91影视

85鈥�90 ? Factor the expression completely. (This type of expression arises in calculus when using the 鈥減roduct rule.鈥�) $$ 5\left(x^{2}+4\right)^{4}(2 x)(x-2)^{4}+\left(x^{2}+4\right)^{5}(4)(x-2)^{3} $$

Distances between Powers \(\quad\) Which pair of numbers is closer together? $$ 10^{10} \text { and } 10^{50} \quad \text { or } \quad 10^{100} \text { and } 10^{101} $$

85鈥�90 ? Factor the expression completely. (This type of expression arises in calculus when using the 鈥減roduct rule.鈥�) $$ 3(2 x-1)^{2}(2)(x+3)^{1 / 2}+(2 x-1)^{3}\left(\frac{1}{2}\right)(x+3)^{-1 / 2} $$

\(83-88=\) Rationalize the numerator. $$ \sqrt{x^{2}+1}-x $$

85鈥�90 ? Factor the expression completely. (This type of expression arises in calculus when using the 鈥減roduct rule.鈥�) $$ \frac{1}{3}(x+6)^{-2 / 3}(2 x-3)^{2}+(x+6)^{1 / 3}(2 x-3)(2) $$

85鈥�90 ? Factor the expression completely. (This type of expression arises in calculus when using the 鈥減roduct rule.鈥�) $$ \left(x^{2}+3\right)^{-1 / 3}-\frac{2}{3} x^{2}\left(x^{2}+3\right)^{-4 / 3} $$

\(89-96\) m State whether the given equation is true for all values of the variables. (Disregard any value that makes a denominator zero.) $$ \frac{16+a}{16}=1+\frac{a}{16} $$

\(89-96\) m State whether the given equation is true for all values of the variables. (Disregard any value that makes a denominator zero.) $$ \frac{b}{b-c}=1-\frac{b}{c} $$

85鈥�90 ? Factor the expression completely. (This type of expression arises in calculus when using the 鈥減roduct rule.鈥�) $$ \frac{1}{2} x^{-1 / 2}(3 x+4)^{1 / 2}+\frac{3}{2} x^{1 / 2}(3 x+4)^{-1 / 2} $$

(a) Show that \(a b=\frac{1}{2}\left[(a+b)^{2}-\left(a^{2}+b^{2}\right)\right] .\) (b) Show that \(\left(a^{2}+b^{2}\right)^{2}-\left(a^{2}-b^{2}\right)^{2}=4 a^{2} b^{2}.\) (c) Show that \(\left(a^{2}+b^{2}\right)\left(c^{2}+d^{2}\right)=(a c+b d)^{2}+(a d-b c)^{2}.\) (d) Factor completely: \(4 a^{2} c^{2}-\left(a^{2}-b^{2}+c^{2}\right)^{2}.\)