Question

Please help being timed!

The variables A, B, and C represent polynomials where A = x2, B = 3x + 2, and C = x – 3. What is AB – C2 in simplest form?

A. 3x3 + 2x2 – x + 3
B. 3x3 + 2x2 – x – 3
C. 3x3 + x2 – 6x + 9
D. 3x3 + x2 + 6x – 9

Answer 1

Step-by-step explanation:

Answer:-

Given:-

• Variables A,B and C.
• With specified values.

Concept:-

Placement and Breaking of Brackets I.e parenthesis.

Let's Do!

$\sf{AB - C^2}$

• A = x2,
• B = 3x + 2, and
• C = x – 3

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

$(3 {x}^{3} + 2 {x}^{2} ) - ( {x}^{2} + 9 - 6x)$

Now, negative sign outside changes the sign inside:-

$= (3 {x}^{3} + 2 {x}^{2} - {x}^{2} - 9 + 6x)$

$= 3 {x}^{3} + {x}^{2} + 6x - 9$

So, D Part is the correct answer.

Note that:-

• The simplest form of equations are formed when they are arranged in sequential form.
• Do arrange them in decreasing order of polynomial degrees.

Answer 2

Answer:

✯ Given :-

• The variables A,B and C represent polynomial where A = x², B = 3x + 2, and C = x - 3.

✯ To Find :-

• What is the simplest form of AB - C².

✯ Solution :-

Given :-

• A = x²
• B = 3x + 2
• C = x - 3

➣ According to the question,

➙ AB - C²

By putting the value we get,

⇒ x²(3x + 2) - (x - 3)²

⇒ 3x² + 2x² - (x² - 6x + 9)

⇒ 3x³ + 2x² - x² + 6x - 9

➠ 3x³ + x² + 6x - 9

$\therefore$ The simplest form of AB - C² is 3x³ + x² + 6x - 9 (Option no D)

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