단항식과 다항식의 계산

In the following exercises, multiply the binomials. Use any method.

$(6pq-3)(4pq-5)$

Simplify: $8x+3x.$

Subtract: $(5n+8)-(2n-1).$

Evaluate: $4{y}^{2}$ when $y=5$

Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial:

• ⓐ $\,8{x}^{2}-7x-9$
• ⓑ $\,-5{a}^{4}$
• ⓒ $\,{x}^{4}-7{x}^{3}-6{x}^{2}+5x+2$
• ⓓ $\,11-4{y}^{3}$
• ⓔ $\,n$

Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial.

• ⓐ $\,z$
• ⓑ $\,2{x}^{3}-4{x}^{2}-x-8$
• ⓒ $\,6{x}^{2}-4x+1$
• ⓓ $\,9-4{y}^{2}$
• ⓔ $\,3{x}^{7}$

Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial.

• ⓐ $\,{y}^{3}-8$
• ⓑ $\,9{x}^{3}-5{x}^{2}-x$
• ⓒ $\,{x}^{4}-3{x}^{2}-4x-7$
• ⓓ $\,-{y}^{4}$
• ⓔ $\,w$

Find the degree of the following polynomials:

• ⓐ $\,4x$
• ⓑ $\,3{x}^{3}-5x+7$
• ⓒ $\,-11$
• ⓓ $\,-6{x}^{2}+9x-3$
• ⓔ $\,8x+2$

Find the degree of the following polynomials:

• ⓐ $\,-6y$
• ⓑ $\,4x-1$
• ⓒ $\,3{x}^{4}+4{x}^{2}-8$
• ⓓ $\,2{y}^{2}+3y+9$
• ⓔ $\,-18$

Find the degree of the following polynomials:

• ⓐ $\,47$
• ⓑ $\,2{x}^{2}-8x+2$
• ⓒ $\,{x}^{4}-16$
• ⓓ $\,{y}^{5}-5{y}^{3}+y$
• ⓔ $\,9{a}^{3}$

Add: $17{x}^{2}+6{x}^{2}.$

Add: $12{x}^{2}+5{x}^{2}.$

Add: $-11{y}^{2}+8{y}^{2}.$

Subtract: $11n-(-8n).$

Subtract: $9n-(-5n).$

Subtract: $-7{a}^{3}-(-5{a}^{3}).$

Simplify: ${a}^{2}+4{b}^{2}-7{a}^{2}.$

Add: $3{x}^{2}+3{y}^{2}-5{x}^{2}.$

Add: $2{a}^{2}+{b}^{2}-4{a}^{2}.$

Find the sum: $(4{x}^{2}-5x+1)+(3{x}^{2}-8x-9).$