Question

Write down the product of −8x²y⁶ and −20xy. Verify the product for x = 2.5, y = 1.

Answer 1

To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e.,​ $a^m\times a^n=a^{m+n}$.

We have:

$$\begin{gathered} \left(-8x^2{y}^6\right)\times \left(-20xy\right) \\ =\left\{\left(-8\right)\times \left(-20\right)\right\}\times \left(x^2\times x\right)\times \left(y^6\times y\right) \\ =\left\{\left(-8\right)\times \left(-20\right)\right\}\times \left(x^{2+1}\right)\times \left(y^{6+1}\right) \\ =-160x^3{y}^7 \end{gathered}$$
$\therefore$ $\left(-8x^2{y}^6\right)\times \left(-20xy\right)=-160x^3{y}^7$

Substituting x = 2.5 and y = 1 in LHS, we get:

$$\begin{gathered} \text{LHS}=\left(-8x^2{y}^6\right)\times \left(-20xy\right) \\ =\left\{-8{\left(2.5\right)}^2{\left(1\right)}^6\right\}\times \left\{-20\left(2.5\right)\left(1\right)\right\} \\ =\left\{-8\left(6.25\right)\left(1\right)\right\}\times \left\{-20\left(2.5\right)\left(1\right)\right\} \\ =\left(-50\right)\times \left(-50\right) \\ =2500 \end{gathered}$$

Substituting x = 2.5 and y = 1 in RHS, we get:​

$$\begin{gathered} \text{RHS}=-160x^3{y}^7 \\ =-160{\left(2.5\right)}^3{\left(1\right)}^7 \\ =-160\left(15.625\right)\times 1 \\ =-2500 \end{gathered}$$

Because LHS is equal to RHS, the result is correct.

Thus, the answer is $-160x^3{y}^7$.