Question

Your friend factors the expression. Is your friend correct? Explain your reasoning.

$16\mathrm{p}-28=4(4\mathrm{p}-28)$

Answer 1

Verfying the factorisation of expression :

The given expression is $(16\mathrm{p}-28)$

The terms of the expression are $\left(16\mathrm{p}\right),\left(28\right)$.

Now, factor the terms of given algebraic expression

$\begin{array}{rcl}16\mathrm{p}& =& 4\times 4\times \mathrm{p}\\ 28& =& 4\times 7\end{array}$

Using the distributive property to factor out the common term $4$

$\begin{array}{rcl}16-28& =& 4\left(4\mathrm{p}\right)-4\left(7\right)\{\mathrm{Rewrite}\mathrm{the}\mathrm{expression}\}\\ & =& 4(4\mathrm{p}-7)\{\mathrm{Distribution}\mathrm{property}\}\end{array}$

Since, $16\mathrm{p}-28=4(4\mathrm{p}-7)\ne 4(4\mathrm{p}-28)$

Therefore, my friend is not correct as we get our answer as $\left[4\right(4\mathrm{p}-7\left)\right]$ friend got $4(4\mathrm{p}-28)$