(a%5E2-3a%2B7)%2B10.jpeg "(a^2-3a)(a^2-3a+7)+10")
Simplifying the Expression: (a^2 - 3a)(a^2 - 3a + 7) + 10
This expression involves a combination of multiplication and addition. Let's break it down step by step:
1. Recognizing the Pattern
Notice that the first part of the expression, (a^2 - 3a), appears twice. This suggests a substitution could simplify the process.
2. Substitution
Let's substitute x = (a^2 - 3a). Our expression now becomes:
x(x + 7) + 10
3. Expanding and Simplifying
Expanding the expression:
x^2 + 7x + 10
Now, we can factor this quadratic expression:
(x + 5)(x + 2)
4. Resubstitution
Substituting back x = (a^2 - 3a):
(a^2 - 3a + 5)(a^2 - 3a + 2)
5. Final Result
Therefore, the simplified form of the expression (a^2 - 3a)(a^2 - 3a + 7) + 10 is (a^2 - 3a + 5)(a^2 - 3a + 2).