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Factorise Completely: 6ab - 3ac A. 3a(2b - c) B. 3(2ab - ac) C. ca(6b - 3c) D. 6a(b - c)

Mathematics

ScanSolve AI Answer

Answer

A

Step-by-step solution

6 steps

To factorise the expression 6ab−3ac6ab - 3ac completely, we need to find the greatest common factor (GCF) of the terms.

  1. Identify the terms in the expression.

    The terms are 6ab6ab and −3ac-3ac.

  2. Find the greatest common factor of the numerical coefficients.

    The coefficients are 6 and 3. The GCF of 6 and 3 is 3.

  3. Find the greatest common factor of the variables.

    Both terms contain the variable aa.
    The first term has bb, but the second term does not.
    The second term has cc, but the first term does not.
    So, the common variable factor is aa.

  4. Combine the numerical and variable GCFs to find the overall GCF.

    The GCF of $6ab$ and $3ac$ is $3a$.

  5. Divide each term in the original expression by the GCF.

    For the first term: 6ab3a=2b\frac{6ab}{3a} = 2b
    For the second term: −3ac3a=−c\frac{-3ac}{3a} = -c

  6. Write the factored expression by placing the GCF outside the parentheses and the results from Step 5 inside.

    3a(2b−c)3a(2b - c)

    Comparing this result with the given options:
    A. 3a(2b−c)3a(2b-c)
    B. 3(2ab−ac)3(2ab-ac)
    C. ca(6b−3c)ca(6b-3c)
    D. 6a(b−c)6a(b-c)

    The correct option is A.

    The final answer is A. 3a(2b−c)\boxed{\text{A. } 3a(2b-c)}.

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