Final answer:
Expanding is multiplying over brackets to remove parentheses, collecting like terms involves combining similar terms, rearranging is changing the order of terms in an equation, and solving equations gives the values that make an equation true.
Step-by-step explanation:
Expand (multiply over brackets): Expanding, or multiplying over brackets, is a mathematical technique used to remove parentheses in an expression. This is done by multiplying each term inside the brackets by the term outside the brackets. For example, if we have the expression 2(x + 3), we would expand it to 2x + 6.
Collecting like terms: Collecting like terms involves combining similar terms in an expression. Terms with the same variables and exponents are considered like terms. For example, in the expression 3x + 2x + 5, we can collect the like terms 3x and 2x to get 5x.
Rearranging: Rearranging, or rearranging equations, refers to changing the order of terms in an equation to isolate a variable or make it the subject of the equation. This is done by applying inverse operations to both sides of the equation. For example, if we have the equation 2x + 5 = 10, we can rearrange it to solve for x by subtracting 5 from both sides to get 2x = 5, and then dividing both sides by 2 to obtain x = 2.5.
Solving equations: Solving equations involves finding the value(s) of the variable(s) that make the equation true. This is done by applying mathematical operations to isolate the variable. For example, if we have the equation 2x + 3 = 7, we can solve for x by subtracting 3 from both sides to get 2x = 4, and then dividing both sides by 2 to obtain x = 2.