Question

Simplify the following using distributive property
(i) $15\times 35+545$

(ii) $97\times 228+36\times 194$

(iii) $29\times 64+18\times 58$

(iv) $0.55\times 0.55-0.55\times 1.5+0.75\times 0.75$

(v) $7+77+777+79+7799+777\times 999$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)15\times 35+5\times 45 \\ =5\times 3\times 35+5\times 45 \\ =5\times 105+5\times 45 \\ =5\left(105+45\right) \\ =5\left(150\right) \\ =750 \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right)97\times 28+36\times 194 \\ =97\times 2\times 14+36\times 194 \\ =194\times 14+36\times 194 \\ =194\left(14+36\right) \\ =194\left(50\right) \\ =9700 \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right)29\times 64+18\times 58 \\ =29\times 2\times 32+18\times 58 \\ =58\times 32+18\times 58 \\ =58\left(32+18\right) \\ =58\left(50\right) \\ =2900 \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iv}\right)0.55\times 0.55-0.55\times 1.5+0.75\times 0.75 \\ ={\left(0.55\right)}^2-0.55\times 2\times 0.75+{\left(0.75\right)}^2 \\ ={\left(0.55\right)}^2-0.55\times 0.75-0.55\times 0.75+{\left(0.75\right)}^2 \\ =0.55\left(0.55-0.75\right)-0.75\left(0.55-0.75\right) \\ =\left(0.55-0.75\right)\left(0.55-0.75\right) \\ ={\left(0.55-0.75\right)}^2 \\ ={\left(-0.20\right)}^2 \\ =0.04 \end{gathered}$$

$$\begin{gathered} \left(\mathrm{v}\right)7+77+777+7\times 9+77\times 99+777\times 999 \\ =7+7\times 9+77+77\times 99+777+777\times 999 \\ =7\left(1+9\right)+77\left(1+99\right)+777\left(1+999\right) \\ =7\left(10\right)+77\left(100\right)+777\left(1000\right) \\ =70+7700+777000 \\ =784770 \end{gathered}$$