Question

for In the given​ expression, calculate as indicated. Express your answer as a single polynomial in standard form. 4x^(3)-2x^(2)+9)-(6x^(2)-6x+5), what is the answer

Answer 1

Answer:

The polynomial in standard form is $y = 14 + 6\cdot x - 8\cdot x^{2}+4\cdot x^{3}$.

Step-by-step explanation:

A polynomial in standard fulfills the following condition:

$y = \Sigma_{i=0}^{m}\,c_{i}\cdot x^{i}$, $\forall\,i\in \mathbb{N}$, $0 \leq i \leq m$

Let be $y = (4\cdot x^{3}-2\cdot x^{2}+9)-(6\cdot x^{2}-6\cdot x + 5)$, which is now handled algebraically:

1) $(4\cdot x^{3}-2\cdot x^{2}+9)-(6\cdot x^{2}-6\cdot x + 5)$ Given

2) $(4\cdot x^{3}-2\cdot x^{2}+9) +(-1)\cdot (6\cdot x^{2}-6\cdot x + 5)$  $(-1)\cdot a = -a$

3) $(4\cdot x^{3}-2\cdot x^{2}+9) +[(-1)\cdot (6\cdot x^{2})+(-6\cdot x)\cdot (-1)+5]$ Definition of substraction/Distributive property

4) $(4\cdot x^{3}-2\cdot x^{2}+9)+(-6\cdot x^{2}+6\cdot x + 5)$  $(-1)\cdot a = -a$/ $(-a)\cdot (-b) = a\cdot b$

5) $4\cdot x^{3}+ (-2\cdot x^{2}-6\cdot x^{2})+6\cdot x + (9+5)$ Associative and commutative properties

6) $4\cdot x^{3}-8\cdot x^{2}+6\cdot x + 14$ Distributive property/Definition of addition

7) $14 + 6\cdot x -8\cdot x^{2}+4\cdot x^{3}$ Commutative property/Result

The polynomial in standard form is $y = 14 + 6\cdot x - 8\cdot x^{2}+4\cdot x^{3}$.