Question

Using the distributive property, Marta multiplied the binomial (2x + 3) by the trinomial (x2 + x – 2) and got the expression below.

Answer 1

The resultant expression is
`2x^(2)+5x^(2)-x-6`.

Explanation:

The distributive property of multiplication is:

`a* (b+c)=(a* b)+(a* c)`

The two polynomials provided are:

`(2x+3)\\(x^(2)+x-2)`

Determine the final expression by multiplying the two polynomials as follows:

`(2x+3)* (x^(2)+x-2)=[2x*(x^(2)+x-2)]+[3*(x^(2)+x-2)]`

`=[(2x* x^(2))+(2x* x)-(2x* 2)]+[(3* x^(2))+(3* x)-(3* 2)]\\\\=[2x^(3)+2x^(2)-4x]+[3x^(2)+3x-6]\\\\=2x^(3)+2x^(2)+3x^(2)-4x+3x-6\\\\=2x^(3)+5x^(2)-x-6`

Thus, the resultant expression is
`2x^(2)+5x^(2)-x-6`.