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Date:___________________

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High School Mathematics
6.18 Homogeneous Expressions

Homogeneous Expression:
If all the terms of an algebraic expression are of the same degree, then such an expression is called homogeneous expression
We denote the coefficients by a, b, c, d, ...etc. and the variables x, y, z.

Example:
ax2 + 2hxy + by2 is a homogeneous expression as every term in it is of second degree. We call this a second degree homogeneous expression in x and y, where x and y are variables and a, h and b are constants.

Homogeneous Expressions

Variables Degree Standard Form
x, y 1 ax + by
x, y 2 ax2 + bxy + cy2
x, y 3 ax3 + bx2y + cxy2 + dy3
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x, y, z 1 ax + by + cz
x, y, z 2 ax2 + by2 + cz2 + dxy + eyz + fzx
x, y, z 3 ax3 + by3 + cz3 + dx2y + exy2 + fy2z + gyz2 + hz2x + kzx2 + lxyz

Directions: Answer the following questions. Also write at least 5 examples of homogeneous expressions of your own.

Name: ___________________

Date:___________________

High School Mathematics
6.18 Homogeneous Expressions

Q 1: 3x + 4y + 5, is this a homogeneous equation?
true
false

Q 2: 5x2 + 7y2 + 5z2, is this a homogeneous equation?
false
true

Q 3: 4x22 + xy + 3y2, is this a homogeneous equation?
true
false

Q 4: 5x + 3y+ 15y2, is this a homogeneous equation?
true
false

Q 5: 3x3 + 5xy2 + 3y3, is this homogeneous equation?
true
false

Q 6: 3x3 - 6x2y + 3xy2 + 7y3, is this a homogeneous equation?
true
false

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Question 8: This question is available to subscribers only!


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