2-solution.jpeg "(x+2y+4z)2 Solution")
Solving the Expression: (x+2y+4z)²
When we encounter an expression like (x+2y+4z)², we can use the binomial theorem to expand it. In this article, we will explore the process of solving this expression and find its expanded form.
Binomial Theorem
The binomial theorem is a mathematical formula for expanding powers of a binomial, which is an expression consisting of two terms. The general formula for the binomial theorem is:
(a+b)ⁿ = aⁿ + naⁿ⁻¹b + n(n-1)aⁿ⁻²b² + ... + n(n-1)(n-2)...(2)(1)abⁿ⁻¹ + bⁿ
where a and b are the two terms, and n is the power to which the binomial is raised.
Applying the Binomial Theorem
Now, let's apply the binomial theorem to our expression (x+2y+4z)². Since we are raising the binomial to the power of 2, we can use the simplified formula:
(a+b)² = a² + 2ab + b²
In our case, a = x, b = 2y+4z, and n = 2. Substituting these values, we get:
(x+2y+4z)² = x² + 2x(2y+4z) + (2y+4z)²
Expanding the Expression
Now, let's expand the expression further:
x² + 2x(2y+4z) + (2y+4z)² = x² + 4xy + 8xz + 4y² + 16yz + 16z²
And that's the final answer! We have successfully expanded the expression (x+2y+4z)² using the binomial theorem.
Conclusion
In this article, we have demonstrated the step-by-step process of solving the expression (x+2y+4z)² using the binomial theorem. By applying the theorem and expanding the expression, we have arrived at the final answer: x² + 4xy + 8xz + 4y² + 16yz + 16z².
