To simplify the expression [tex]\(6x(x + y) - 2(x + y)\)[/tex] step-by-step, let's proceed with the algebraic simplification:
Step 1: Start with the given expression:
[tex]\[ 6x(x + y) - 2(x + y) \][/tex]
Step 2: Notice that both terms contain the factor [tex]\((x + y)\)[/tex]. We can factor [tex]\((x + y)\)[/tex] out of both terms to simplify:
[tex]\[ 6x(x + y) - 2(x + y) = (x + y) \cdot (6x - 2) \][/tex]
Step 3: Therefore, the simplified form of the expression is:
[tex]\[ (x + y) \cdot (6x - 2) \][/tex]
However, breaking it down into products or distributing terms does not simplify further beyond factorization. So our simplified expression remains:
[tex]\[ 6x(x + y) - 2(x + y) \][/tex]
So the original expression [tex]\(6x(x + y) - 2(x + y)\)[/tex] simplifies to [tex]\((x + y) \cdot (6x - 2)\)[/tex], which aligns with the result we reviewed.
Thus, we conclude that the simplified form is:
[tex]\[ 6x(x + y) - 2x - 2y \][/tex]
