SaiBook.us Math

Home Course Section Lesson

Lesson Topics Discussion Quiz: Class Homework

Example1

Title: Multiplying Polynomials

Grade 8+ Lesson s1-l2

Explanation: The best way to understand algebra is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1

Find the product of \$(2x^2 − 3x + 1)\$ and (3x + 2).

Step 1

The given polynomial \$(2x^2 − 3x + 1)\$ and (3x + 2)
Let’s start multiplying:
\$2x^2\$ multiplied by 3x: \$2x^2 \times 3x\$ = \$6x^3\$
\$2x^2\$ multiplied by 2: \$2x^2 \times 2\$ = \$4x^2\$
-3x multiplied by 3x: \$-3x \times 3x \$ = \$-9x^2\$
-3x multiplied by 2: \$-3x \times 2\$ = - 6x
1 multiplied by 3x: \$1 \times 3x\$ = 3x
1 multiplied by 2: \$ 2 \times 1\$ = 2

Explanation:

This involves multiplying every term in the polynomial by each term in the polynomial expression to expand it fully.

Step 2

Now, let’s add up all the results:
\$6x^3 + 4x^2 - 9x^2 - 6x +3x +2\$

Combining like terms:
\$6x^3 − 5x^2 − 3x + 2\$

So, the product of \$(2x^2 − 3x + 1)\$ and (3x+2) is \$6x^3 − 5x^2 − 3x + 2\$.

Explanation:

Multiply each term, sum the products, and then consolidate the terms to obtain the final result.