<span>a2 – b2 = (a + b)(a – b) or (a – b)(a + b).
This is the 'Difference of Squares' formula we can use to factor the expression.
In order to use the </span><span>'Difference of Squares' formula to factor a binomial, the binomial must contain two perfect squares that are separated by a subtraction symbol.
</span><span>x^2 - 4 fits this, because x^2 and 4 are both perfect squares, and they are separated by a subtraction symbol.
All you do here to factor, is take the square root of each term.
√x^2 = x
√4 = 2
Now that we have our square roots, x and 2, we substitute these numbers into the form (a + b)(a - b).
</span>
<span>(a + b)(a - b)
(x + 2)(x - 2)
Our answer is final </span><span>(x + 2)(x - 2), which can also be written as (x - 2)(x + 2), it doesn't make a difference which order you put it in.
Anyway, Hope this helps!!
Let me know if you need help understanding anything and I'll try to explain as best I can.</span>
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
Answer:
The system has zero solutions.
The correct answer would be option number 2
