Match each algebraic expression on the left with its equivalent simplified form on the rig… — ACT

Match each algebraic expression on the left with its equivalent simplified form on the right. Assume all variables represent real numbers.

The expression

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

matches

3a^2 - 2b

;

a(3a - b) - 2b(a - b)

matches

3a^2 - 3ab + 2b^2

;

(a + b)(3a - 2b) - b^2

matches

3a^2 + ab - 3b^2

; and

4a^2 - (a - b)(a + 2b) - 2b^2

matches

3a^2 - ab

Each expression is correctly simplified by distributing coefficients, expanding binomial products, and collecting like terms.

Simplify the expression

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

3a^2 - 2b

Distribute the coefficients to remove the parentheses:

6a^2 - 8b - 3a^2 + 6b

. Group the

a^2

terms and the

b

terms, and then combine:

(6 - 3)a^2 + (-8 + 6)b = 3a^2 - 2b

Simplify the expression

a(3a - b) - 2b(a - b)

3a^2 - 3ab + 2b^2

Distribute the variables

a

and

-2b

3a^2 - ab - 2ab + 2b^2

. Combine the like terms

-ab

and

-2ab

to get

-3ab

, resulting in

3a^2 - 3ab + 2b^2

Simplify the expression

(a + b)(3a - 2b) - b^2

3a^2 + ab - 3b^2

Multiply the binomial factors using the distributive property:

(a + b)(3a - 2b) = 3a^2 - 2ab + 3ab - 2b^2 = 3a^2 + ab - 2b^2

. Subtract the remaining

b^2

term:

3a^2 + ab - 2b^2 - b^2 = 3a^2 + ab - 3b^2

Simplify the expression

4a^2 - (a - b)(a + 2b) - 2b^2

3a^2 - ab

Expand

(a - b)(a + 2b) = a^2 + ab - 2b^2

. Subtract this product from

4a^2

by distributing the negative sign:

4a^2 - a^2 - ab + 2b^2

. Finally, subtract the last term

2b^2

3a^2 - ab + 2b^2 - 2b^2 = 3a^2 - ab

Simplifying algebraic expressions by distributing factors and combining like terms

Estimated Time:2m 0s

Question