Simplify the following algebraic expression completely by distributing and combining like … — Armed Services Vocational Aptitude Battery (ASVAB)

Simplify the following algebraic expression completely by distributing and combining like terms:

3a(2a - 4b) - 2b(a - 5b)

Answer: 6a^2 - 14ab + 10b^2 / 6a^2-14ab+10b^2 / 10b^2 - 14ab + 6a^2 / 6a^2+10b^2-14ab / 6a^2 - 14ba + 10b^2

6a^2 - 14ab + 10b^2

The expression is correctly simplified by first applying the distributive property to both parts:

3a(2a - 4b)

becomes

6a^2 - 12ab

, and

-2b(a - 5b)

becomes

-2ab + 10b^2

. Next, the like terms (

-12ab

and

-2ab

) are combined to form

-14ab

. The resulting expression in standard form is

6a^2 - 14ab + 10b^2

Distribute

3a

across the terms in the first parenthesis

(2a - 4b)

6a^2 - 12ab

Applying the distributive property to eliminate the first set of parentheses.

Distribute

-2b

across the terms in the second parenthesis

(a - 5b)

-2ab + 10b^2

Multiplying by a negative requires changing the signs. Specifically,

(-2b) \times (-5b) = +10b^2

Write out the full expanded expression and identify like terms.

6a^2 - 12ab - 2ab + 10b^2

Preparing to combine terms with identical variable parts.

Combine the like terms (

-12ab

and

-2ab

6a^2 - 14ab + 10b^2

-12 - 2 = -14

, resulting in the final simplified standard form.

Distributive Property and Combining Like Terms with Multiple Variables

Question