Simplify the following algebraic expressions: 1. (2x2 + y) − (x2 + 2y3) 2. 12x2/3xy 3. 6b3/3b

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

: $(2x^2 + y) - (x^2 + 2y^3)$

Distribute the negative sign to the terms inside the second parenthesis.
$2x^2 + y - x^2 - 2y^3$
Combine like terms.
$(2x^2 - x^2) + y - 2y^3$ $x^2 + y - 2y^3$
The terms $y$ and $-2y^3$ are not like terms, so they cannot be combined further.

The simplified expression is $\boxed{x^2 + y - 2y^3}$ .

: $\frac{12x^2}{3xy}$
Simplify the numerical coefficients.
$\frac{12}{3} = 4$
Simplify the variables using the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ .
$\frac{x^2}{x} = x^{2-1} = x^1 = x$ $\frac{1}{y}$
Combine the simplified parts.
$4 \cdot x \cdot \frac{1}{y} = \frac{4x}{y}$
The simplified expression is $\boxed{\frac{4x}{y}}$ .

: $\frac{6b^3}{3b}$
Simplify the numerical coefficients.
$\frac{6}{3} = 2$
Simplify the variables using the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ .
$\frac{b^3}{b} = b^{3-1} = b^2$
Combine the simplified parts.
$2 \cdot b^2 = 2b^2$
The simplified expression is $\boxed{2b^2}$ .

Simplify the following algebraic expressions: 1. (2x2 + y) - (x2 + 2y3) 2. (12x2)/(3xy) 3. (6b3)/(3b)