Operations with Polynomials

Do you want to know how to solve Operations with Polynomials? you can do it in one easy steps.

Step by step guide to do Operations with Polynomials

• When multiplying a monomial by a polynomial, use the distributive property.
$$\color{blue}{a×(b+c)=a×b+a×c}$$
• For adding and subtracting polynomials remember to find and combine like terms.

Example 1:

Multiply. $$4(3x-5)-4x=$$

Solution:

Use the distributive property: $$4(3x−5)= 12x−20$$

Now, combine like terms: $$4(3x-5)-4x=12x-20-4x=8x-20$$

Example 2:

Multiply. $$6x(3x+7)+12x-x^2=$$

Solution:

Use the distributive property: $$6x(3x+7)=18x^2+42x$$

Cobine like terms: $$6x(3x+7)+12x-x^2= 18x^2+42x+12x-x^2=17x^2+54x$$

Example 3:

Multiply. $$5(2x-6)-x^2+4x=$$

Solution:

Use the distributive property: $$5(2x-6)=10x-30$$

Now, combine like terms: $$5(2x-6)-x^2+4x= 10x-30 -x^2+4x=-x^2+14x-30$$

Example 4:

Multiply. $$2x(6x+2)=$$

Solution:

Use the distributive property: $$2x(6+2)=12x^2+4x$$

Exercises

Find each product.

1. $$\color{blue}{3x^2 (6x – 5)+12x}$$
2. $$\color{ blue }{5x^2 (7x – 2)-x^2}$$
3. $$\color{blue}{– 3 (8x – 3)+5x}$$
4. $$\color{blue}{6x^3 (– 3x + 4)-2x^2}$$
5. $$\color{blue}{9 (6x + 2)+14x+8}$$
6. $$\color{blue}{8 (3x + 7)-x^4}$$

1. $$\color{blue}{18x^3 – 15x^2+12x}$$
2. $$\color{ blue }{35x^3 – 11x^2}$$
3. $$\color{blue}{–19x + 9}$$
4. $$\color{blue}{–18x^4 + 24x^3-2x^2}$$
5. $$\color{blue}{68x + 26}$$
6. $$\color{blue}{-x^4+24x + 56}$$

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