Question

Identify the terms & coefficients for the following expression.

$4x^2{y}^2-4x^2{y}^2{z}^2+z^2$

• A. $Terms:4x^2{y}^2,-4x^2{y}^2{z}^2,z^2$$Coefficients:4,-4,1$
• B. $Terms:4x{y}^2,-4x^2{y}^2{z}^2,z^2$$Coefficients:4,-4,1$
• C. $Terms:4x^2{y}^2,-4x^{2}y{z}^2,z^2$$Coefficients:4,-4,1$
• D. $Terms:4x^2{y}^2,-4x^2{y}^2{z}^2,z^2$$Coefficients:4,4,1$

Answer 1

The correct option is A $Terms:4x^2{y}^2,-4x^2{y}^2{z}^2,z^2$

$Coefficients:4,-4,1$

We know that each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables. Each term in an algebraic expression is separated by a positive sign or a negative sign.

For example, in the expression $4x^2{y}^2-4x^2{y}^2{z}^2+z^2$, the terms are: $4x^2{y}^2,-4x^2{y}^2{z}^2$ and $z^2$.

Also, when a term is made up of a constant multiplied by a variable or variables, that constant is called a coefficient.

For example, in the expression $4x^2{y}^2-4x^2{y}^2{z}^2+z^2$, the coefficients are: $4,-4$ and $1$.

Hence, the terms are $4x^2{y}^2,-4x^2{y}^2{z}^2,z^2$ and the coefficients are $4,-4,1$.