Match each unsimplified algebraic expression on the left with its correctly simplified for… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each unsimplified algebraic expression on the left with its correctly simplified form on the right.

$4m + 7m - 2$ $11m - 2$
$3(2m + 5)$ $6m + 15$
$9m - (4m - 3)$ $5m + 3$
$m(2m - 1)$ $2m^2 - m$

Answer

The correct matches pair each unsimplified expression with its corresponding simplified form: 4m + 7m - 2 pairs with 11m - 2; 3(2m + 5) pairs with 6m + 15; 9m - (4m - 3) pairs with 5m + 3; and m(2m - 1) pairs with 2m^2 - m.

Each unsimplified expression is paired with its mathematically equivalent simplified form by correctly applying standard algebraic rules: combining like terms and utilizing the distributive property.

Step-by-Step Solution

Simplify the first expression by identifying and combining like terms.

4m + 7m - 2 = 11m - 2

The terms 4m and 7m have the exact same variable part and can be added together.

Simplify the second expression by applying the distributive property.

3(2m + 5) = 6m + 15

The outside factor of 3 must be multiplied by every term contained inside the parentheses.

Simplify the third expression by distributing the negative sign, then combining the resulting like terms.

9m - 4m + 3 = 5m + 3

Subtracting a grouped polynomial requires reversing the sign of each term within the group.

Simplify the fourth expression by multiplying the variable through the parentheses.

m(2m - 1) = 2m^2 - m

Multiplying a variable by itself increases its exponent based on the laws of exponents.

Key Concept

Simplifying Algebraic Expressions

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