Here we need to use algebraic properties to simplify an expression, we will get:
[tex]7\cdot (-9\cdot a + 2\cdot a + 8) - 3\cdot a = -52\cdot a + 56[/tex]
The mathematical property we need to use is the distributive property.
[tex]A\cdot (B + C) = A\cdot B + A \cdot C[/tex]
So we start with the expression:
[tex]7\cdot (-9\cdot a + 2\cdot a + 8) - 3\cdot a[/tex]
First, we use the distributive property in the first term so we get:
[tex]7\cdot (-9\cdot a + 2\cdot a + 8) - 3\cdot a \\\\= 7\cdot (-9)\cdot a + 7\cdot 2 \cdot a + 7 \cdot8 - 3\cdot a\\\\= -63 \cdot a + 14\cdot a + 56 - 3\cdot a[/tex]
Now we use the distributive property in the other way, we take "a" as a common factor:
[tex]-63 \cdot a + 14\cdot a + 56 - 3\cdot a\\\\= (-63 + 14 - 3)\cdot a + 56\\\\= -52\cdot a + 56[/tex]
Here we got the simplified expression.
If you want to learn more, you can read:
https://brainly.com/question/403991
