Ex.9.2 Q3 Algebraic Expressions and Identities - NCERT Maths Class 8

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Question

Complete the table of products.

\(\begin{align}\frac{{{\rm{First}}\,{\rm{monomial}} \to }}{{{\rm{Second}}\,{\rm{monomial}} \downarrow }}\end{align}\) \(2x\) \( - 5y\) \(3{x^2}\) \( - 4xy\) \(7{x^2}y\) \( - 9{x^2}{y^2}\)
\(2x\) \(4{x^2}\) \( \dots \) \( \dots \) \( \dots \) \( \dots \) \( \dots \)
\( - 5y\) \( \dots \) \( \dots \) \( - 15{x^2}y\) \( \dots \) \( \dots \) \( \dots \)
\(3{x^2}\) \( \dots \) \( \dots \) \( \dots \) \( \dots \) \( \dots \) \( \dots \)
\( - 4xy\) \( \dots \) \( \dots \) \( \dots \) \( \dots \) \( \dots \) \( \dots \)
\(7{x^2}y\) \( \dots \) \( \dots \) \( \dots \) \( \dots \) \( \dots \) \( \dots \)
\( - 9{x^2}{y^2}\) \( \dots \) \( \dots \) \( \dots \) \( \dots \) \( \dots \) \( \dots \)

Text Solution

What is known?

Expressions

What is Unknown?

Product

Steps:

The table can be completed as follows.

\(\begin{align}\frac{{{\rm{First}}\,{\rm{monomial}} \to }}{{{\rm{Second}}\,{\rm{monomial}} \downarrow }}\end{align}\) \(2x\) \( - 5y\) \(3{x^2}\) \( - 4xy\) \(7{x^2}y\) \( - 9{x^2}{y^2}\)
\(2x\) \(4{x^2}\) \( - 10xy\) \(6{x^3}\) \( - 8{x^2}y\) \(14{x^3}y\) \( - 18{x^3}{y^2}\)
\( - 5y\) \( - 10xy\) \(25{y^2}\) \( - 15{x^2}y\) \(20x{y^2}\) \( - 35{x^2}{y^2}\) \(45{x^2}{y^3}\)
\(3{x^2}\) \(6{x^3}\) \( - 15{x^2}y\) \(9{x^4}\) \( - 12{x^3}y\) \(21{x^4}y\) \( - 27{x^4}{y^2}\)
\( - 4xy\) \( - 8{x^2}y\) \(20x{y^2}\) \( - 12{x^3}y\) \(16{x^2}{y^2}\) \( - 28{x^3}{y^2}\) \(36{x^3}{y^3}\)
\(7{x^2}y\) \(14{x^3}y\) \( - 35{x^2}{y^2}\) \(21{x^4}y\) \( - 28{x^3}{y^2}\) \(49{x^4}{y^2}\) \( - 63{x^4}{y^3}\)
\( - 9{x^2}{y^2}\) \( - 18{x^3}{y^2}\) \(45{x^2}{y^3}\) \( - 27{x^4}{y^2}\) \(36{x^3}{y^3}\) \( - 63{x^4}{y^3}\) \(81{x^4}{y^4}\)
  
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