단항식과 다항식의 계산

Find the sum: $(3{x}^{2}-4xy+5{y}^{2})+(2{x}^{2}-xy)$.

Find the sum: $(2{x}^{2}-3xy-2{y}^{2})+(5{x}^{2}-3xy)$.

Find the difference: $({p}^{2}+{q}^{2})-({p}^{2}+10pq-2{q}^{2})$.

Find the difference: $({a}^{2}+{b}^{2})-({a}^{2}+5ab-6{b}^{2})$.

Find the difference: $({m}^{2}+{n}^{2})-({m}^{2}-7mn-3{n}^{2})$.

Simplify: $({a}^{3}-{a}^{2}b)-(a{b}^{2}+{b}^{3})+({a}^{2}b+a{b}^{2})$.

Simplify: $({x}^{3}-{x}^{2}y)-(x{y}^{2}+{y}^{3})+({x}^{2}y+x{y}^{2})$.

Simplify: $({p}^{3}-{p}^{2}q)+(p{q}^{2}+{q}^{3})-({p}^{2}q+p{q}^{2})$.

Evaluate $5{x}^{2}-8x+4$ when

• ⓐ $x=4$
• ⓑ $x=-2$
• ⓒ $x=0$

Evaluate: $3{x}^{2}+2x-15$ when

• ⓐ $x=3$
• ⓑ $x=-5$
• ⓒ $x=0$

Evaluate: $5{z}^{2}-z-4$ when

• ⓐ $z=-2$
• ⓑ $z=0$
• ⓒ $z=2$

Identify Polynomials, Monomials, Binomials, and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

ⓐ $81{b}^{5}-24{b}^{3}+1$ ⓑ $5{c}^{3}+11{c}^{2}-c-8$ ⓒ $\frac{14}{15}y+\frac{1}{7}$

ⓓ 5

ⓔ $4y+17$

Identify Polynomials, Monomials, Binomials, and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

ⓐ ${x}^{2}-{y}^{2}$ ⓑ $-13{c}^{4}$ ⓒ ${x}^{2}+5x-7$ ⓓ ${x}^{2}{y}^{2}-2xy+8$ ⓔ 19

Identify Polynomials, Monomials, Binomials, and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

ⓐ $8-3x$ ⓑ ${z}^{2}-5z-6$ ⓒ ${y}^{3}-8{y}^{2}+2y-16$ ⓓ $81{b}^{5}-24{b}^{3}+1$ ⓔ $-18$

Identify Polynomials, Monomials, Binomials, and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

ⓐ $11{y}^{2}$ ⓑ $-73$ ⓒ $6{x}^{2}-3xy+4x-2y+{y}^{2}$ ⓓ $4y+17$ ⓔ $5{c}^{3}+11{c}^{2}-c-8$

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

ⓐ $6{a}^{2}+12a+14$ ⓑ $18x{y}^{2}z$ ⓒ $5x+2$ ⓓ ${y}^{3}-8{y}^{2}+2y-16$ ⓔ $-24$

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

ⓐ $9{y}^{3}-10{y}^{2}+2y-6$ ⓑ $-12{p}^{4}$ ⓒ ${a}^{2}+9a+18$ ⓓ $20{x}^{2}{y}^{2}-10{a}^{2}{b}^{2}+30$ ⓔ 17

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

ⓐ $14-29x$ ⓑ ${z}^{2}-5z-6$ ⓒ ${y}^{3}-8{y}^{2}+2y-16$ ⓓ $23a{b}^{2}-14$ ⓔ $-3$

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

ⓐ $62{y}^{2}$ ⓑ 15 ⓒ $6{x}^{2}-3xy+4x-2y+{y}^{2}$ ⓓ $10-9x$ ⓔ ${m}^{4}+4{m}^{3}+6{m}^{2}+4m+1$

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

${\,\text{7x}}^{2}+5{x}^{2}$