Respuesta :

Accoding to the distributive property,

[tex](a+b)\ast(c+d)=a\ast(c+d)+b\ast(c+d)[/tex]

a.

Apply the property to the given expression,

[tex]\begin{gathered} (x+2)(x+9) \\ =x\mleft(x+9\mright)+2\mleft(x+9\mright) \\ =x^2+9x+2x+18 \\ =x^2+11x+18 \end{gathered}[/tex]

Thus, the given equivalent expression is,

[tex]x^2+11x+18[/tex]

b.

Apply the property to the given expression,

[tex]\begin{gathered} (x+4)(2x-1) \\ =x(2x-1)+2(2x-1) \\ =2x^2-x+4x-2 \\ =2x^2+3x-2 \end{gathered}[/tex]

Thus, the given equivalent expression is,

[tex]2x^2+3x+2[/tex]

c.

To apply the Distributive Property, we need a 3rd term. But here are only two terms in the expression.

So the only other possible way to write the equation using Distributive property is given as,

[tex]\begin{gathered} (x-5) \\ =1(x-5) \\ =1(x)-1(5) \end{gathered}[/tex]

Thus, the required equivalent expression is ,

[tex]1(x)-1(5)[/tex]