R 2x + 8 8x – 4 Q T S l
The Correct Answer and Explanation is:
Your question seems to involve an algebraic expression, possibly an equation or a simplification problem. However, the expression you’ve given is incomplete or unclear:
“R 2x + 8 8x – 4 Q T S”
Let’s try to interpret it in a meaningful way.
It might be that you’re referring to simplifying or solving something like:
Possible Intended Expression:
(2x + 8)(8x – 4)
This is a product of two binomials and can be expanded using the distributive property (FOIL method).
Step-by-step Solution:
(2x + 8)(8x – 4)
Use the distributive property (FOIL):
- First: 2x × 8x = 16x²
- Outer: 2x × (-4) = -8x
- Inner: 8 × 8x = 64x
- Last: 8 × (-4) = -32
Now add all these together:
16x² – 8x + 64x – 32
Combine like terms:
16x² + 56x – 32
Final Answer:
16x² + 56x – 32
Explanation:
To simplify an algebraic expression involving the product of two binomials, we apply the distributive property—commonly remembered by the acronym FOIL (First, Outer, Inner, Last). In this case, we have:
(2x + 8)(8x – 4)
The process involves multiplying each term in the first binomial by each term in the second. The first terms, 2x and 8x, multiply to give 16x², which is the highest degree term and represents the quadratic part of the expression. Next, we multiply the outer terms: 2x and -4, giving -8x. This represents one part of the linear component.
Then we handle the inner terms: 8 and 8x, resulting in 64x, which adds to the linear term. Lastly, we multiply the constants (last terms) 8 and -4 to get -32, which is the constant in the final simplified expression.
After computing all four products, we combine like terms. The two middle terms, -8x and 64x, are like terms and sum to 56x. So the simplified expression becomes:
16x² + 56x – 32
This result is a quadratic trinomial in standard form, which is ax² + bx + c, where:
- a = 16 (coefficient of x²),
- b = 56 (coefficient of x),
- c = -32 (constant).
This form is useful in algebra for factoring, solving quadratic equations, or graphing the corresponding parabola.
