Simplify each.

26. \frac{2(12x - 10)}{4} + \frac{10(3x + 2)}{5}

27. \frac{2a(a + 4)}{a} - \frac{2a(3a - 4)}{2a}

To simplify these expressions, we will distribute, combine like terms, and simplify fractions when possible.

4 2 ( 12 x − 10 ) ​ + 5 10 ( 3 x + 2 ) ​

Step 1: Distribute the numbers outside the parentheses.

For 4 2 ( 12 x − 10 ) ​ : 4 2 × 12 x − 2 × 10 ​ = 4 24 x − 20 ​

For 5 10 ( 3 x + 2 ) ​ : 5 10 × 3 x + 10 × 2 ​ = 5 30 x + 20 ​


Step 2: Simplify the fractions.

4 24 x − 20 ​ = 6 x − 5
5 30 x + 20 ​ = 6 x + 4

Step 3: Add the simplified expressions.

6 x − 5 + 6 x + 4 = 12 x − 1

So, the simplified expression for 26 is 12 x − 1 .

a 2 a ( a + 4 ) ​ − 2 a 2 a ( 3 a − 4 ) ​

Step 1: Simplify each fraction.

For a 2 a ( a + 4 ) ​ , we can divide each term by a (assuming a  = 0 ): a 2 a ( a + 4 ) ​ = 2 ( a + 4 ) = 2 a + 8

For 2 a 2 a ( 3 a − 4 ) ​ : 2 a 2 a ( 3 a − 4 ) ​ = 3 a − 4 (since 2 a cancels with 2 a )


Step 2: Subtract the expressions.

( 2 a + 8 ) − ( 3 a − 4 ) = 2 a + 8 − 3 a + 4
Combine like terms: − a + 12

So, the simplified expression for 27 is − a + 12 .

Answered by DanielJosephParker | 2025-07-06