Question

d="TexFormula1" title="\frac{x^{2} -1}{16x} X \frac{4x^{2} }{5x + 5}" alt="\frac{x^{2} -1}{16x} X \frac{4x^{2} }{5x + 5}" align="absmiddle" class="latex-formula">

Answer 1

Answer:

x^2-x / 20

Step-by-step explanation:

Answer 2

$\underline{\underline{\large\bf{Solution:-}}}$

$\begin{gathered}\\\implies\quad \sf \frac{x^{2} -1}{16x} \times \frac{4x^{2} }{5x + 5} \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf \frac{\cancel{(x+1)}(x-1)}{16x} \times \frac{4x^{2} }{5\cancel{(x + 1)}} \quad\quad(a^2-b^2 = (a+b)(a-b))\\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf \frac{x-1}{\cancel{16x}} \times \frac{\cancel4x^{\cancel2} }{5} \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf \frac{(x -1)(x)}{4\times 5} \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf \frac{x^2-x}{20} \\\end{gathered}$

More Identities:-

$\begin{gathered}\boxed{\sf{ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \: }} \\ \end{gathered}$

$\begin{gathered}\boxed{\sf{ {(a - b)}^{2} = {a}^{2} + {b}^{2} -2ab \: }} \\ \end{gathered}$

$\begin{gathered}\boxed{\sf{ {x}^{2} - {y}^{2} = (x + y)(x - y) \: }} \\ \end{gathered}$

$\begin{gathered}\boxed{\sf {(a + b)² = (a - b)² + 4ab\: }} \\ \end{gathered}$

$\begin{gathered}\boxed{\sf {(a - b)² = (a + b)² - 4ab\: }} \\ \end{gathered}$

$\begin{gathered}\boxed{\sf {(a + b)² + (a - b)² = 2(a² + b²)\: }} \\ \end{gathered}$

$\begin{gathered}\boxed{\sf{ (a + b)³ = a³ + b³ + 3ab(a + b)\: }} \\ \end{gathered}$

$\begin{gathered}\boxed{\sf {(a - b)³ = a³ - b³ - 3ab(a - b)\: }} \\ \end{gathered}$