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Distribution in algebra, often referred to as the distributive property, is a fundamental technique used to simplify expressions. This technique is especially useful when dealing with expressions involving parentheses.
When you encounter an expression like \(a(b + c)\), distribution allows you to multiply each term inside the parentheses by \(a\). Hence, \(a(b + c)\) becomes \(ab + ac\).
In our example, the expression is \(3(7x^2 - 2x) - 3\). Here, we distribute the 3 by multiplying it with each term inside the parentheses:

• \(3 \times 7x^2 = 21x^2\)
• \(3 \times -2x = -6x\)

After applying distribution, the expression transforms into \(21x^2 - 6x - 3\).
This method ensures that no part of the expression is overlooked and helps in maintaining the balance and equality of equations.

Simplification is the process of condensing an algebraic expression to its simplest form. This involves removing any unnecessary components and making the expression as concise as possible.
The expression we are dealing with, after distribution, is \(21x^2 - 6x - 3\). The simplification process here includes ensuring all like terms are combined and any constants or similar terms are condensed.
In some cases, you may see opportunities to combine like terms. However, this expression doesn't have like terms. Thus, it is already simplified.
Simplification follows two main steps:

• Combining like terms (if any are present).
• Reducing constants or coefficients if possible.

Even though no further action was needed here, being thorough with the simplification process ensures accuracy in mathematical operations.

Like terms are terms whose variables and their exponents are the same. Recognizing like terms is crucial in the simplification and overall manipulation of polynomials.
For example, in the expression \(2x^2 + 3x^2 + x - 4x\), \(2x^2\) and \(3x^2\) are like terms because they both have the variable \(x^2\); likewise, \(x\) and \(-4x\) share the same variable \(x\).
Adding or subtracting like terms helps to simplify expressions by condensing them into fewer terms.
In the given problem \(21x^2 - 6x - 3\), there are no like terms to combine. Each term \(21x^2\), \(-6x\), and \(-3\) has a distinct variable component or none at all.
It's important to distinguish these so you can accurately reduce expressions and solve equations efficiently.