Question

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Answer 1

Homogeneous Expression

→   A homogeneous expression is an expression or a polynomial of usually more than one variable in which each term has the same degree obtained by adding powers of each variable used in the term.

E.g.: $\sf{3x^4+5x^3y+2xy^3+y^4}$ is a homogeneous expression as the degree of each term in the expression is 4.

• Degree of $\sf{3x^4=4.}$

• Degree of $\sf{5x^3y=3+1=4}$

• Degree of $\sf{2xy^3=1+3=4}$

• Degree of $\sf{y^4=4.}$

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In the expression $\sf{4x^2-5xy+5x^2y+10y^2,}$ the degree of $\sf{5x^2y}$ is 3 but that of others is 2 each. Hence it is not a homogeneous expression.

In the expression $\sf{5x+10y+100,}$ since neither the variable x nor y is with 100, we can say that its degree is 0. But other terms have a degree of 1 each. Hence it is not a homogeneous expression.

In the expression $\sf{14x^3+15x^2y+16y^2x+24y^3,}$ each term has a degree of 3, hence it is a homogeneous equation.

In the expression $\sf{x^2+y^2+x+y+1,}$ we can see three different degrees, 0, 1 and 2. Hence it is not a homogeneous expression.

Hence $\sf{\underline{\underline{(c)\ 14x^3+15x^2y+16y^2x+24y^3}}}$ is the answer.