To express the quadratic expression x² + 4x as a square of a binomial, we can use the formula:
(a + b)² = a² + 2ab + b²
If we can find values for a and b such that 2ab = 4x, then we can write:
x² + 4x = x² + 2(ab)x + (b²)
The first term is x², so we want a² to be equal to x². Therefore, a = x.
Now we need to find b such that 2ab = 4x. We can simplify this equation to ab = 2x, and since we already know a = x, we can substitute and solve for b:
x * b = 2x
b = 2
So we have:
x² + 4x = x² + 2(x*2) + 2² = (x+2)²
Therefore, x² + 4x can be expressed as the square of the binomial (x+2).
Answers & Comments
Information:
Answerer: GenuisPanda
Date Posted: March 17, 2023
Topic: Binomials
Answer:
To express the quadratic expression x² + 4x as a square of a binomial, we can use the formula:
If we can find values for a and b such that 2ab = 4x, then we can write:
The first term is x², so we want a² to be equal to x². Therefore, a = x.
Now we need to find b such that 2ab = 4x. We can simplify this equation to ab = 2x, and since we already know a = x, we can substitute and solve for b:
So we have:
Therefore, x² + 4x can be expressed as the square of the binomial (x+2).