Rules for multiplication

ImportantTo do

• Read §3 Rules for multiplication
• Before each proof of N6–N10: cover it, try it yourself
• §3 exercises: 1 a c e, ★2, ★3, 4, 6, 8, …, 28 (even), 30, 32
• Weak spot (diagnostic 4): signs when you expand. Check every sign twice
• Paper: all listed exercises. Mark ✓ / ✗ / S. Answers: back of the book.
• Notebook: write each div below in your own words. Copy the ★ exercises in clean.

Definition 1 (Distributivity (distributivita)) Your words.

Theorem 1 (N6: multiplication by 1 and 0) Your words.

Proof. Cover the book’s proof. Try 10–15 min first.

Theorem 2 (N7–N9: minus signs in products) Your words.

Proof. Cover the book’s proof. Try 10–15 min first.

Theorem 3 (N10: (−a)(−b) = ab) Your words.

Proof. Cover the book’s proof. Try 10–15 min first.

Definition 2 (Power (mocnina)) Your words.

Theorem 4 (N11–N12: exponent (exponent) rules) Your words.

Proof. Cover the book’s proof. Try 10–15 min first.

TipIntuition

Your words.

Exercises

★ 2. Prove: (a + b)^3 = a^3 + 3a^2 b + 3ab^2 + b^3 and (a - b)^3 = a^3 - 3a^2 b + 3ab^2 - b^3.

NoteSolution

Your words.

★ 3. Expand (a + b)^4 and (a - b)^4.

NoteSolution

Your words.