Multiply coefficients and variables separately: $(2 \times -3 \times 4) \times (x \times y \times z) = -24xyz$.

Question 1

What is the coefficient of $x^2$ in the algebraic expression $3x^2y - 5x + 7$?

Accepted Answer

In the term $3x^2y$, the numerical and literal multipliers of $x^2$ are $3$ and $y$. Thus, the coefficient of $x^2$ is $3y$.

Question 2

Which of the following algebraic expressions is a binomial?

Accepted Answer

An algebraic expression containing exactly two unlike terms is called a binomial. Here, $2x + 3y$ has two unlike terms.

Question 3

What is the sum of the like terms $5x^2$ and $7x^2$?

Accepted Answer

To add like terms, we add their numerical coefficients: $5x^2 + 7x^2 = (5 + 7)x^2 = 12x^2$.

Question 4

Find the product of the monomials: $2x$, $-3y$, and $4z$.

Accepted Answer

Multiply coefficients and variables separately: $(2 	imes -3 	imes 4) 	imes (x 	imes y 	imes z) = -24xyz$.

Question 5

Using identity $(a + b)^2 = a^2 + 2ab + b^2$, expand $(2x + 3y)^2$.

Accepted Answer

Here, $a = 2x$ and $b = 3y$. $(2x + 3y)^2 = (2x)^2 + 2(2x)(3y) + (3y)^2 = 4x^2 + 12xy + 9y^2$.

Algebraic Expressions and Identities