Respuesta :

Explanation

We need to simplify this product of expressions:

[tex](3x+3)\cdot(4x-6)[/tex]

We must use the distributive property of the multiplication here. We take the left expression and we multiply both terms of the right expression by it:

[tex](3x+3)\cdot(4x-6)=(3x+3)\cdot4x+(3x+3)\cdot(-6)[/tex]

Now we have the sum of two expressions. We apply the distributive property of the multiplication to both:

[tex](3x+3)\cdot4x+(3x+3)\cdot(-6)=3x\cdot4x+3\cdot4x+3x\cdot(-6)+3\cdot(-6)[/tex]

We continue operating:

[tex]3x\cdot4x+3\cdot4x+3x\cdot(-6)+3\cdot(-6)=12x^2+12x-18x-18[/tex]

We can use the distributive property inversely in the terms with x:

[tex]\begin{gathered} 12x^2+12x-18x-18=12x^2+(12-18)\cdot x-18 \\ 12x^2+(12-18)\cdot x-18=12x^2-6x-18 \end{gathered}[/tex]Answer

Then the answer is:

[tex]12x^2-6x-18[/tex]

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