Question

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

Answer 1

Answer:

The resultant expression is $2x^{2}+5x^{2}-x-6$.

Step-by-step explanation:

The distributive property of multiplication is:

$a\times (b+c)=(a\times b)+(a\times c)$

The two polynomials provided are:

$(2x+3)\\(x^{2}+x-2)$

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

$(2x+3)\times (x^{2}+x-2)=[2x\times(x^{2}+x-2)]+[3\times(x^{2}+x-2)]$

$=[(2x\times x^{2})+(2x\times x)-(2x\times 2)]+[(3\times x^{2})+(3\times x)-(3\times 2)]\\\\=[2x^{3}+2x^{2}-4x]+[3x^{2}+3x-6]\\\\=2x^{3}+2x^{2}+3x^{2}-4x+3x-6\\\\=2x^{3}+5x^{2}-x-6$

Thus, the resultant expression is $2x^{2}+5x^{2}-x-6$.