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GenaCL600 [577]
2 years ago
14

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

Mathematics
1 answer:
romanna [79]2 years ago
6 0

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.

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