Final answer:
The algebraic expression for '10 more than a number f' is 'f + 10', which represents the addition of 10 to the variable f. Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values.
Step-by-step explanation:
The algebraic expression for the word phrase '10 more than a number f' is f + 10. This expression reflects the operation of addition where 10 is added to an unknown number f. In this case, the unknown number is represented by the variable f, and 'more than' indicates that 10 is added to it.
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
To divide two algebraic expressions, we factor the numerator and the denominator, cancel the possible terms, and simplify the rest. Here are some examples of dividing algebraic expressions.
- 2x2 / (2x2 + 4x) = (2x2) / [2x (x + 2)] = x / (x + 2)
- (x2 + 5x + 4) / (x + 1) = [ (x + 4) (x + 1) ] / (x + 1) = x + 4
To multiply two algebraic expressions, we multiply every term of the first expression with every term of the second expression and combine all the products. Here are some examples of multiplying algebraic expressions.
- ab (2ab + 3) = 2a2b2 + 3ab
- (x + 1) (x + 2) = x2 + x + 2x + 2 = x2 + 3x + 2