https://file.aiquickdraw.com/mathbot/file/1726632295024mqaevny7.jpg

The expression in the image appears to be:

\[
42a^2 - 78a + 15b - 5b^2 - 90
\]

Let's factor this expression step by step.

### Step 1: Group terms
We can group terms involving \(a\) and \(b\) separately:

\[
(42a^2 - 78a) + (15b - 5b^2) - 90
\]

### Step 2: Factor each group
#### For the \(a\)-terms:
Factor out the greatest common factor (GCF) from \(42a^2 - 78a\):

\[
42a^2 - 78a = 6a(7a - 13)
\]

#### For the \(b\)-terms:
Factor out the GCF from \(15b - 5b^2\):

\[
15b - 5b^2 = 5b(3 - b)
\]

### Step 3: Combine the terms
After factoring, the expression becomes:

\[
6a(7a - 13) + 5b(3 - b) - 90
\]

### Step 4: Factor the constant term
Now, factor out the constant term \(-90\):

\[
-90 = -90
\]

Thus, the final factorized form of the expression is:

\[
6a(7a - 13) + 5b(3 - b) - 90
\]

Would you like to explore further details about the factorization process?

Here are 5 related questions:
1. Can you apply the same factorization technique to a quadratic equation?
2. How can grouping terms simplify more complex expressions?
3. How do you determine the greatest common factor in each group?
4. What are other factoring methods for higher-degree polynomials?
5. How can we check if the factorization is correct?

**Tip**: Always recheck the factored terms by expanding them back to the original expression to verify the correctness.

Factorise this expression: 42a^2 - 78a + 15b - 5b^2 - 90

Learn how to factorize the expression 42a^2 - 78a + 15b - 5b^2 - 90 step by step. This solution involves algebraic concepts like factoring by grouping and finding the greatest common factor. Suitable for students in Grades 9-12.

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