Step 1: Factorise m² - 16
To factorise the expression m² - 16, we recognize it as a difference of squares. The formula for factoring a difference of squares is:
a² - b² = (a - b)(a + b)
In this case:
- a = m
- b = 4 (since 16 = 4²)
Thus, we factor it as:
- (m - 4)(m + 4)
Step 2: Subtract 6x² - 4xy + 5y² from 8y² + 16xy - 3x²
Let’s first write down the expressions:
- Expression A: 8y² + 16xy - 3x²
- Expression B: 6x² - 4xy + 5y²
Now, we perform the subtraction:
8y² + 16xy - 3x² - (6x² - 4xy + 5y²)
Distributing the negative sign gives:
8y² + 16xy - 3x² - 6x² + 4xy - 5y²
Now, combine like terms:
- For y²: 8y² - 5y² = 3y²
- For xy: 16xy + 4xy = 20xy
- For x²: -3x² - 6x² = -9x²
So, the result is:
3y² + 20xy - 9x²
Step 3: Final Expression
Thus, the final expression after subtraction is:
3y² + 20xy - 9x²
This completes the factorization and subtraction processes!