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:

\[\left( - 8 x^2 y^6 \right) \times \left( - 20xy \right)\]

\[ = \left\{ \left( - 8 \right) \times \left( - 20 \right) \right\} \times \left( x^2 \times x \right) \times \left( y^6 \times y \right)\]

\[ = \left\{ \left( - 8 \right) \times \left( - 20 \right) \right\} \times \left( x^{2 + 1} \right) \times \left( y^{6 + 1} \right)\]

\[ = - 160 x^3 y^7 \]

\[\therefore\] \[\left( - 8 x^2 y^6 \right) \times \left( - 20xy \right) = - 160 x^3 y^7\]

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

\[\text { LHS } = \left( - 8 x^2 y^6 \right) \times \left( - 20xy \right)\]

\[ = \left\{ - 8 \left( 2 . 5 \right)^2 \left( 1 \right)^6 \right\} \times \left\{ - 20\left( 2 . 5 \right)\left( 1 \right) \right\}\]

\[ = \left\{ - 8\left( 6 . 25 \right)\left( 1 \right) \right\} \times \left\{ - 20\left( 2 . 5 \right)\left( 1 \right) \right\}\]

\[ = \left( - 50 \right) \times \left( - 50 \right)\]

\[ = 2500\]

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

\[\text { RHS } = - 160 x^3 y^7 \]

\[ = - 160 \left( 2 . 5 \right)^3 \left( 1 \right)^7 \]

\[ = - 160\left( 15 . 625 \right) \times 1\]

\[ = - 2500\]

Because LHS is equal to RHS, the result is correct.
Thus, the answer is \[- 160 x^3 y^7\].