x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616
<u>Explanation:</u>
We know
(x+y)ⁿ = ∑ ⁿCₐxⁿ⁻ᵃyᵃ
and ⁿCₐ = n! / ( a! ) . ( n-a )!
So,
(x+6)⁸ = ⁸C₀x⁸ + ⁸C₁(x)⁸⁻¹(6)¹ + ⁸C₂(x)⁸⁻²(6)² + ⁸C₃(x)⁸⁻³(6)³ + .......+ ⁸C₈(x)⁸⁻⁸(6)⁸
= ₓ⁸ + 8x⁷ₓ 6 + 28x⁶ₓ 36 + 56x⁵ₓ 216 + 70x⁴ₓ 1296 + 56x³ₓ 7776 + 28x²ₓ 46656 + 8x . 279936 + 1679616
= x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616
Thus, the expansion of ( x+6)⁸ using binomial theorm is
x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616
Answers:
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Work Shown:
The ratio 2 red : 6 grey reduces to 1 red : 3 grey when we divide both parts by 2. For every 1 red car, there are 3 grey cars. There are triple as many grey compared to red.
Let x be the number of red cars. Since there are 3 times as many grey cars, this means 3x represents the number of grey cars.
The total number of cars can be represented by the expression x+3x = 4x
Set this equal to the total number of cars (144) and solve for x
4x = 144
x = 144/4
x = 36
There are 36 red cars.
Subtract that value from 144 to find 144-36 = 108 grey cars.
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An alternative way to solve:
(2 red)/(6 grey) = (x red)/( (144-x) grey)
2/6 = x/(144-x)
2(144-x) = 6x .... cross multiply
2*144 - 2*x = 6x
288 - 2x = 6x
288 = 6x+2x
288 = 8x
8x = 288
x = 288/8
x = 36
If there are 144 vehicles in the parking lot, then 36 cars are red.
Also, 144 - x = 144 - 36 = 108 cars are grey.
Answer:
Associative property of multiplication
Step-by-step explanation:
Associative property of multiplication