Question

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. $3xy^{2}+8xy^{4}+5xy - 2xy^{2}$

degree = ——————————— m b t p

1. $8x^{2}-15x - 21+16x^{2}-4x^{2}y$

degree = ——————————— m b t p

1. $10x^{2}y+3xy - 4xy^{2}-5xy$

degree = ——————————— m b t p

Explanation:

Step1: Combine like terms for \(3xy^{2}+8xy^{4}+5xy - 2xy^{2}\)

Combine the \(xy^{2}\) terms: \((3xy^{2}-2xy^{2})+8xy^{4}+5xy=xy^{2}+8xy^{4}+5xy\). The degree of a term \(ax^{m}y^{n}\) is \(m + n\). For \(xy^{2}\), degree is \(1 + 2=3\); for \(8xy^{4}\), degree is \(1+4 = 5\); for \(5xy\), degree is \(1 + 1=2\). The polynomial in standard form is \(8xy^{4}+xy^{2}+5xy\). It has three terms, but the highest - degree term is \(8xy^{4}\) with degree \(5\).

Step2: Combine like terms for \(8x^{2}-15x - 21+16x^{2}-4x^{2}y\)

Combine the \(x^{2}\) terms: \((8x^{2}+16x^{2})-15x - 21-4x^{2}y=24x^{2}-15x - 21-4x^{2}y\). For \(24x^{2}\), degree is \(2\); for \(-15x\), degree is \(1\); for \(-21\), degree is \(0\); for \(-4x^{2}y\), degree is \(2 + 1=3\). The polynomial in standard form is \(-4x^{2}y+24x^{2}-15x - 21\). The highest - degree term is \(-4x^{2}y\) with degree \(3\).

Step3: Combine like terms for \(10x^{2}y+3xy - 4xy^{2}-5xy\)

Combine the \(xy\) terms: \(10x^{2}y+(3xy - 5xy)-4xy^{2}=10x^{2}y-2xy-4xy^{2}\). For \(10x^{2}y\), degree is \(2 + 1=3\); for \(-2xy\), degree is \(1+1 = 2\); for \(-4xy^{2}\), degree is \(1 + 2=3\). The polynomial in standard form can be written as \(10x^{2}y-4xy^{2}-2xy\) (or other arrangements of the terms with the same degrees). The degree of the polynomial is \(3\).

Answer:

For \(3xy^{2}+8xy^{4}+5xy - 2xy^{2}\): degree \( = 5\), \(T\) (trinomial).
For \(8x^{2}-15x - 21+16x^{2}-4x^{2}y\): degree \(=3\), \(P\) (more than three terms).
For \(10x^{2}y+3xy - 4xy^{2}-5xy\): degree \(=3\), \(T\) (trinomial).