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zhannawk [14.2K]
3 years ago
13

Simplify the expression 2(x + 7)(x2 – 3x – 6).

Mathematics
2 answers:
Oksi-84 [34.3K]3 years ago
7 0

Answer:

2x^3+8x^2-54x-84

Step-by-step explanation:

ivolga24 [154]3 years ago
4 0

Answer:

2(x + 7)(x² - 3x - 6) = 2x³ + 8x² - 54x - 84

Step-by-step explanation:

Simplification is a method used to reduce the complexity or the component parts of an algebraic equation which makes it simpler and easier to understand.

The given equation is: 2(x + 7)(x² - 3x - 6).

Simplifying the given algebraic equation:

⇒ 2 (x + 7) (x² - 3x - 6)

⇒ (2x + 14) (x² - 3x - 6)

⇒ 2x³ + 14x² - 6x² - 42x - 12x - 84

⇒ <u>2x³ + 8x² - 54x - 84</u>

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<u>Given:</u>

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<u>Solution:</u>

There are 4 external surfaces for the rectangular prism and 4 external surfaces for the triangular prism.

The rectangular prism has 4 rectangles out which there are 2 sets of similar rectangles.

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The area of a rectangle with a length of 25 feet and a width of 10 feet = 25(10)= 250 square ft.

The area of two such rectangles = 2(250) = 500 square feet.

The area of a rectangle with a length of 55 feet and a width of 10 feet = 55(10)= 550 square feet.

The area of two such rectangles = 2(550) = 1100 square feet.

The triangular prism has 2 triangles and 2 rectangles.

The triangles have base lengths of 25 feet and heights of 8 feet while the rectangles have lengths of 55 feet and heights of 14.8 feet.

The area of a triangle with a base length of 25 feet and a height of 8 feet = \frac{1}{2}(25)(8)= 100 square feet.

The area of two such triangles =2(100)= 200 square feet.

The area of a rectangle with a length of 55 feet and a width of 14.8 feet = 55(14.8)= 814 square feet.

The area of two such rectangles = 2(814) = 1628 square feet.

The total area to be painted =500+1100+200+1628 = 3128 square feet.

So an area of 3128 square feet is to be painted.

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