Answer:
2[tex]x^{4}[/tex] + x³ - x² + 54x - 56
Step-by-step explanation:
Area (A) is calculated as
A = length × width
= (x² - 2x + 8)(2x² + 5x - 7)
Each term in the second factor is multiplied by each term in the first factor, that is
x²(2x² + 5x - 7) - 2x(2x² + 5x - 7) + 8(2x² + 5x - 7) ← distribute all parenthesis
= 2[tex]x^{4}[/tex] + 5x³ - 7x² - 4x³ - 10x² + 14x + 16x² + 40x - 56 ← collect like terms, thus
A = 2[tex]x^{4}[/tex] +x³ - x² + 54x - 56
The expression which represents the area of Dylan’s room will be 2x⁴ - 7x³ - 21x² + 82x - 56.
What is the area?
The area is the space occupied by any shape, find out by multiplying its length and breadth.
We have,
Lenght = (x² – 2x + 8)
and
Breadth = (2x² + 5x – 7)
Now, simplifying the above expressions,
(x² – 2x + 8)
It can be written as , Using middle term split method,
x² – 4x + 2x + 8
= x(x – 4) - 2(x - 4)
= (x – 4) (x - 2)
In the same way,
(2x² + 5x – 7)
= 2x² +7x - 2x – 7
= x(2x +7) - 1(2x + 7)
= (x - 1) (2x +7)
So,
So,
Using the area formula,
i.e.
Area = Length × Breadth
Area = (x² – 2x + 8) × (2x² + 5x – 7) = (x – 4) (x - 2) (x - 1) (2x +7)
Now,
Area = 2x⁴ - 7x³ - 21x² + 82x - 56
Hence we can say that the expression which represents the area of Dylan’s room will be 2x⁴ - 7x³ - 21x² + 82x - 56.
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