SAT Equivalent Expressions Question 70 | Free SAT Prep | Aniko

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Question 70·Easy·Equivalent Expressions

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Which expression is equivalent to $4k^2 + 9k - 3k^2 + 2k$ ?

For expression-equivalence questions, immediately look for like terms: same variable and same exponent. Rewrite the expression by grouping like terms next to each other, then add or subtract their numerical coefficients while keeping the variable part the same. Pay close attention to plus and minus signs in front of each term, since most mistakes come from ignoring a negative sign or adding when you should subtract. Finally, compare your simplified expression carefully with the answer choices to avoid picking a choice that simplified only part of the expression or combined unlike terms.

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Look for like terms

Which terms have $k^2$ and which have just $k$ ? Group the $k^2$ terms together and the $k$ terms together.

Rewrite by grouping

Rewrite the expression as one pair of $k^2$ terms and one pair of $k$ terms, for example something like (k-squared terms) plus (k terms).

Be careful with signs

When you combine $4k^2$ and $-3k^2$ , are you adding or subtracting their coefficients? Do the same check for $9k$ and $2k$ .

Desmos Guide

Enter the original expression as a function

In Desmos, type f(k) = 4k^2 + 9k - 3k^2 + 2k. This represents the original expression as a function of $k$ .

Enter each answer choice as its own function

For each answer choice, type a new function like g(k) = (expression from choice A), h(k) = (expression from choice B), and so on for choices C and D, using the exact expressions given in the problem.

Compare the graphs

Look at the graphs of all these functions. The choice whose graph lies exactly on top of the graph of $f(k)$ for all values of $k$ is the expression that is equivalent to the original.

Step-by-step Explanation

Identify like terms

Look at the expression $4k^2 + 9k - 3k^2 + 2k$ and group terms that have the same variable and exponent:

The $k^2$ terms are $4k^2$ and $-3k^2$ .
The $k$ terms are $9k$ and $2k$ .

Plan to combine each group separately.

Combine the $k^2$ terms

Combine the $k^2$ terms using their coefficients:

4k^2 - 3k^2 = (4 - 3)k^2 = 1k^2

So the $k^2$ part of the simplified expression is $k^2$ .

Combine the $k$ terms

Now combine the $k$ terms:

9k + 2k = (9 + 2)k = 11k

So the $k$ part of the simplified expression is $11k$ .

Write the final simplified expression and match the choice

Put the simplified parts together:

4k^2 + 9k - 3k^2 + 2k = k^2 + 11k

So the expression is equivalent to $k^2 + 11k$ , which corresponds to choice D.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation