This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To factorise the expression 6ab - 3ac completely, we need to find the greatest common factor (GCF) of the terms. Step 1: Identify the terms in the expression. The terms are 6ab and -3ac. Step 2: Find the greatest common factor of the numerical coefficients. The coefficients are 6 and 3. The GCF of 6 and 3 is 3. Step 3: Find the greatest common factor of the variables. Both terms contain the variable a. The first term has b, but the second term does not. The second term has c, but the first term does not. So, the common variable factor is a. Step 4: Combine the numerical and variable GCFs to find the overall GCF. The GCF of 6ab and 3ac is 3a. Step 5: Divide each term in the original expression by the GCF. For the first term: (6ab)/(3a) = 2b For the second term: (-3ac)/(3a) = -c Step 6: Write the factored expression by placing the GCF outside the parentheses and the results from Step 5 inside. 3a(2b - c) Comparing this result with the given options: A. 3a(2b-c) B. 3(2ab-ac) C. ca(6b-3c) D. 6a(b-c) The correct option is A. The final answer is A. 3a(2b-c). What's next?