Question

Type the correct answer in each box. Consider this expression.

Answer 1

Answer:

The expression is equivalent to  $-4\cdot x^{2}+3\cdot x -5$.

Step-by-step explanation:

In this exercise we must transform $-4\cdot x^{2}+2\cdot x -5\cdot (1+x)$ into its standard form, that is a polynomial of the form:

$y = a\cdot x^{2} + b\cdot x + c$ (1)

Where:

$y$ - Dependent variable.

$x$ - Independent variable.

$a$, $b$, $c$ - Coefficients.

Let $y = -4\cdot x^{2}+2\cdot x -5\cdot (1+x)$, now we proceed to convert it into its standard form:

1) $-4\cdot x^{2}+2\cdot x -5\cdot (1+x)$ Given

2) $(-4)\cdot x^{2}+2\cdot x + (-5)\cdot (1+x)$ $(-a)\cdot b = -a\cdot b$

3) $(-4)\cdot x^{2}+2\cdot x +(-5)\cdot 1 +(-5)\cdot x$ Distributive property

4) $(-4)\cdot x^{2}+[5+(-2)]\cdot x -5$ $(-a)\cdot b = -a\cdot b$/Commutative and distributive properties

5) $-4\cdot x^{2}+3\cdot x -5$ $(-a)\cdot b = -a\cdot b$/Definition of subtraction/Result

The expression is equivalent to  $-4\cdot x^{2}+3\cdot x -5$.