단항식과 다항식의 계산

Multiply a Trinomial by a Binomial

In the following exercises, multiply using ⓐ the Distributive Property and ⓑ the Vertical Method.

$(n+8)(4{n}^{2}+n-7)$

In the following exercises, multiply. Use either method.

$(y-6)({y}^{2}-10y+9)$

In the following exercises, multiply. Use either method.

$(k-3)({k}^{2}-8k+7)$

In the following exercises, multiply. Use either method.

$(2x+1)({x}^{2}-5x-6)$

In the following exercises, multiply. Use either method.

$(5v+1)({v}^{2}-6v-10)$

Mental math You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply $13$ times $15.$ Think of $13$ as $10+3$ and $15$ as $10+5.$

• ⓐ Multiply $(10+3)(10+5)$ by the FOIL method.
• ⓑ Multiply $13\,\cdot \,15$ without using a calculator.
• ⓒ Which way is easier for you? Why?

Mental math You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply $18$ times $17.$ Think of $18$ as $20-2$ and $17$ as $20-3.$

• ⓐ Multiply $(20-2)(20-3)$ by the FOIL method.
• ⓑ Multiply $18\,\cdot \,17$ without using a calculator.
• ⓒ Which way is easier for you? Why?

Which method do you prefer to use when multiplying two binomials—the Distributive Property, the FOIL method, or the Vertical Method? Why?

Which method do you prefer to use when multiplying a trinomial by a binomial—the Distributive Property or the Vertical Method? Why?

Simplify: $8x+3x.$

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

Write in expanded form: ${a}^{5}.$

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

• ⓐ $4{y}^{2}-8y-6$
• ⓑ $-5{a}^{4}{b}^{2}$
• ⓒ $2{x}^{5}-5{x}^{3}-9{x}^{2}+3x+4$
• ⓓ $13-5{m}^{3}$
• ⓔ $q$

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

ⓐ $5b$ ⓑ $8{y}^{3}-7{y}^{2}-y-3$ ⓒ $-3{x}^{2}-5x+9$ ⓓ $81-4{a}^{2}$ ⓔ $-5{x}^{6}$

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

ⓐ $27{z}^{3}-8$ ⓑ $12{m}^{3}-5{m}^{2}-2m$ ⓒ $\frac{5}{6}$ ⓓ $8{x}^{4}-7{x}^{2}-6x-5$ ⓔ $-{n}^{4}$

Find the degree of the following polynomials.

• ⓐ $10y$
• ⓑ $4{x}^{3}-7x+5$
• ⓒ $-15$
• ⓓ $-8{b}^{2}+9b-2$
• ⓔ $8x{y}^{2}+2y$

Find the degree of the following polynomials:

ⓐ $-15b$ ⓑ $10{z}^{4}+4{z}^{2}-5$ ⓒ $12{c}^{5}{d}^{4}+9{c}^{3}{d}^{9}-7$ ⓓ $3{x}^{2}y-4x$ ⓔ $-9$

Find the degree of the following polynomials:

ⓐ $52$ ⓑ ${a}^{4}b-17{a}^{4}$ ⓒ $5x+6y+2z$ ⓓ $3{x}^{2}-5x+7$ ⓔ $-{a}^{3}$

Add: $25{y}^{2}+15{y}^{2}$.

Add: $12{q}^{2}+9{q}^{2}.$