Question

Identify and write the like terms in each of the following groups.
\[ - x{y^2}, - 4y{x^2},8{x^2},2x{y^2},7y, - 11{x^2} - 100x, - 11yx,20{x^2}y, - 6{x^2},y,2xy,3x\]

Answer 1

Hint:The terms having the same variable with same exponents are called like terms. Check the variables and exponents of all the variables. Then the terms with the similar exponents and variables will come under like terms.

Complete step-by-step answer:
Let us consider the given terms,
Here, the given terms are \[ - x{y^2}, - 4y{x^2},8{x^2},2x{y^2},7y, - 11{x^2} - 100x, - 11yx,20{x^2}y, - 6{x^2},y,2xy,3x\] and amongst these terms. We have checked among the all there is any same literal (variable) in the terms. If there are any terms on it. It is like a term. Let's check with the terms who choose randomly.
Take the terms \[7y\] and \[y\],
\[7y\] and \[y\] are like terms. Since they contain the same variable \[y\] to the same power, the power \[y\] of is 1 in both terms. Therefore the terms \[7y\] and \[y\] are like terms.
Take the terms \[ - 11yx\] and \[2xy\],
 \[ - 11yx\] and \[2xy\] are like terms. Since they contain the same variable \[x\] and \[y\] to the same power, the power of \[x\] is 1 and the power of \[y\] is also 1. Therefore the terms \[ - 11yx\] and \[2xy\] are like terms
Take the terms \[8{x^2}\] and \[ - 6{x^2}\],
 \[8{x^2}\] and \[ - 6{x^2}\]are like terms. Since they contain the same variable \[x\] to the same power, the powers of \[x\] is 2 in both terms. Therefore the terms \[8{x^2}\] and \[ - 6{x^2}\] are like terms.
Take the terms \[ - 4y{x^2}\] and \[20{x^2}y\],\[2x{y^2}\]
 \[ - 4y{x^2}\] and \[20{x^2}y\] are like terms. Since they contain the same variable \[x\] and \[y\] to the same power, the powers of \[x\] is 2 and the power of \[y\] is 1. Therefore the terms \[ - 4y{x^2}\] and \[20{x^2}y\] are like terms.
Also, \[ - x{y^2}\] and are like terms. Since they contain the same variable \[x\] and \[y\] to the same power, the powers of \[y\] is 2 and the power of \[x\] is 1. Therefore the terms \[ - x{y^2}\] and \[2x{y^2}\] are also like terms.
Hence, the like terms are \[\left( {7y,y} \right),\left( {8{x^2}, - 6{x^2}} \right),\left( { - 11yx,2xy} \right),\left( { - x{y^2},2x{y^2}} \right),and\left( { - 4y{x^2},20{x^2}y} \right)\]

Note:We know that like terms are terms that contain the same variables raised to the same exponent (power). Only the numerical coefficients are different.
Constants are always said to be like terms because in every constant term there may be any number of variables which have the exponent zero.
Unlike terms are the terms which have different variables and exponents.