To multiply polynomials, you follow these steps: 1. Group the numerical coefficients and literal coefficients together. 2. Multiply the numerical coefficients. 3. Apply the laws of exponents to simplify the expression.

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by:g. Martin

2. To multiply the polynomials, we follow the following rules:
• Apply the associative law for multiplication. Group the numerical
coefficients and the literal coefficients together.
• Multiply the numerical coefficients.
• Apply the law of exponents.

3. Example 1. Simplify (x3) (x2).
= (x3) (x2)
= x3+2 (Apply the product rule)
= x5 (Simplify)

4. Example 2. Multiply (3x2) (2x).
= (3x2) (2x)
= (3 . 2) (x2 . x) (Group numerical coefficient and literal coefficient
together)
= (6) . (x3)
= (6x3)

5. Example 3. Multiply (x2y)( x2y(2y3).
= (x2y)(x2y)(2y3)
= (x2)(x2) . (y . y . y3) . (2) (Group numerical and literal coefficient
together).
= (x4) . (y5) .(2)
= 2x4y5

6. Example 4. Multiply (-2xy) (-3x2y).
= (-2xy) (-3x2y)
= (-2 . -3) . (x . x2) . (y . y) (Group numerical and literal
coefficient)
= (6) . (x3) . (y2)
= 6x3y2

7. Example 5. Simplify (3a2)2 (a4)
= (3a2)2 (a4)
= (3a2) (3a2) . (a4)
= (3. 3) (a2 . a2 . a4) (Group numerical and literal coefficient)
= (9) (a8)
= 9a8