Question

Rewrite each expression using the Distributive Property. The simplify,

$\mathbf{-}\mathbf{6}\mathbf{(}{\mathbf{x}}^{\mathbf{2}}\mathbf{-}\mathbf{5}\mathbf{x}\mathbf{+}\mathbf{6}\mathbf{)}$

Short answer

By the Distributive property the expression is simplified as:

$-6(x-3)(x-2)$

Step-by-step solution

Step 1. State the concept for distributive property.

The distributive property states that any expression with three numbers A, B and C, given in form $A(B+C)$then it is resolved as $A\times (B+C)=AB+AC$or $A(B-C)=AB-AC$.

This means operand A is distributed among the other two operands.

This property is also known as the distributivity of multiplication over addition or subtraction.

Step 2. Rewrite the given expression.

Solving the given equation:
$\begin{array}{c}-6(x^2-5x+6)=-6(x^2-3x-2x+6)\\ =-6(x(x-3)-2(x-3))\\ =-6(x-3)(x-2)\end{array}$

Step 3. Conclusion.

Therefore, by the Distributive property the expression is simplified as:
$-6(x-3)(x-2)$