## Related Topics

- How to Multiply Monomials
- How to Multiply and Dividing Monomials
- How to Multiply Binomials
- How to Factor Trinomials
- How to Add and Subtract Polynomials

## 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.

### Operations with Polynomials – Example 1:

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

**Solution:**

Use the distributive property: \(\color{blue}{a×(b+c)=a×b+a×c}\)

Then: \(4(3x−5)= 12x−20\)

Now, combine like terms: \(12x-4x=8x\)

Then simplify: \(4(3x-5)-4x=12x-20-4x=8x-20\)

**Operations with Polynomials – Example 2: **

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

**Solution:**

Use the distributive property: \(\color{blue}{a×(b+c)=a×b+a×c}\)

Then: \(6x(3x+7)=18x^2+42x\)

Now, combine like terms: \(18x^2-x^2=17x^2\) , \(42x+12x=54x\)

Then simplify: \(6x(3x+7)+12x-x^2= 18x^2+42x+12x-x^2=17x^2+54x\)

### Operations with Polynomials – Example 3:

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

**Solution:**

Use the distributive property: \(\color{blue}{a×(b+c)=a×b+a×c}\)

Then: \(5(2x-6)=10x-30 \)

Now, combine like terms: \( 10x+4x=14x\)

Then simplify: \(5(2x-6)-x^2+4x= 10x-30 -x^2+4x=-x^2+14x-30\)

### Operations with Polynomials – Example 4:

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

**Solution:**

Use the distributive property: \(\color{blue}{a×(b+c)=a×b+a×c}\)

Then: \(2x(6x+2)=12x^2+4x \)

## Exercises for Solving Operations with Polynomials

### Find each product.

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

### Download Operations with Polynomials Worksheet

- \(\color{blue}{18x^3 – 15x^2+12x}\)
- \(\color{ blue }{35x^3 – 11x^2}\)
- \(\color{blue}{–19x + 9}\)
- \(\color{blue}{–18x^4 + 24x^3-2x^2}\)
- \(\color{blue}{68x + 26}\)
- \(\color{blue}{-x^4+24x + 56}\)

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