Question

spiral review
combine like terms. write the answer in correct standard form.
then list the degree and circle m for monomial, b for binomial,
t for trinomial or p if there are more than three terms.
1
10ab - 4ab² + 26a²b - 15ab - 7a²b
degree =
m b t p
2
19abc - 3ab²c - 18abc + 3abc² - abc
degree =
m b t p
3
-42y² - 7x² + 16y² - 8x² + 15
degree =
m b t p

Explanation:

Step1: Combine like terms for the first expression

For \(10ab - 4ab^{2}+26a^{2}b - 15ab - 7a^{2}b\), combine \(10ab-15ab=-5ab\) and \(26a^{2}b - 7a^{2}b = 19a^{2}b\). The simplified expression is \(-4ab^{2}+19a^{2}b - 5ab\). The degree of a term is the sum of the exponents of the variables. For \(-4ab^{2}\) (degree \(1 + 2=3\)), \(19a^{2}b\) (degree \(2+1 = 3\)), \(-5ab\) (degree \(1+1=2\)). The highest degree is \(3\).

Step2: Combine like terms for the second expression

For \(19abc-3ab^{2}c - 18abc+3abc^{2}-abc\), combine \(19abc-18abc - abc=0\). The simplified expression is \(-3ab^{2}c+3abc^{2}\). For \(-3ab^{2}c\) (degree \(1 + 2+1=4\)) and \(3abc^{2}\) (degree \(1+1 + 2=4\)). The highest degree is \(4\).

Step3: Combine like terms for the third expression

For \(-42y^{2}-7x^{2}+16y^{2}-8x^{2}+15\), combine \(-42y^{2}+16y^{2}=-26y^{2}\) and \(-7x^{2}-8x^{2}=-15x^{2}\). The simplified expression is \(-26y^{2}-15x^{2}+15\). For \(-26y^{2}\) (degree \(2\)), \(-15x^{2}\) (degree \(2\)), \(15\) (degree \(0\)). The highest degree is \(2\).

Answer:

1. degree \( = 3\), B (binomial as there are three terms after combining but wait no: \(-4ab^{2}+19a^{2}b - 5ab\) is a trinomial (T).
2. degree \(=4\), B (binomial: \(-3ab^{2}c + 3abc^{2}\)).
3. degree \(=2\), T (trinomial: \(-26y^{2}-15x^{2}+15\)).