Simplifying a polynomial sum with like terms in one line

Key takeaway: This is the same core skill as the preceding problem: combining like terms. The difference here is that the prompt emphasizes the final answer entry, so accuracy in the simplified form matters most.

Start by rewriting the expression cleanly

The expression is

$$(8y^2-4y)+(7y^2-9y+7).$$

Because the operation between the parentheses is addition, you can remove the parentheses without changing any signs. That gives the horizontal form

$$8y^2-4y+7y^2-9y+7.$$

Combine matching terms

Now group terms by type:

• quadratic terms: $8y^2$ and $7y^2$
• linear terms: $-4y$ and $-9y$
• constant term: $7$

Add the coefficients of the like terms:

$$8y^2+7y^2=15y^2,$$ $$-4y-9y=-13y.$$

The constant stays $7$, so the simplified expression is

$$15y^2-13y+7.$$

Check the structure of the final answer

A well-simplified polynomial should be written with like terms combined and no unnecessary parentheses. In this case, there should be exactly three terms in the result. If you see anything other than $15y^2-13y+7$, it usually means one of the signs was handled incorrectly or a pair of like terms was missed.

Quick rule to remember

When parentheses are joined by plus, nothing changes inside them. That is the easiest way to avoid a sign error. Then add coefficients only after matching the variable and exponent. This simple pattern works for nearly every polynomial simplification problem at this level.

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Pitfalls the pros know 👇 Students often rush and combine the coefficients before checking whether the terms are actually like terms. For example, $8y^2$ and $-4y$ cannot be added together because one is quadratic and the other is linear. Another mistake is dropping the plus sign before the final constant or writing $15y^2-13y+7$ as $15y^2+13y+7$. The negative sign on the $y$ term matters and comes from adding two negative linear coefficients. Reading the terms aloud can help catch that error before submitting.

What if the problem changes? If the second parentheses had been written with a minus sign, such as $(8y^2-4y)-(7y^2-9y+7)$, then you would need to distribute the negative first. The result becomes $8y^2-4y-7y^2+9y-7$, which simplifies to $y^2+5y-7$. That variant is useful because it shows the difference between addition of polynomials and subtraction of a polynomial expression.

Tags: like terms, horizontal form, polynomial expression