We Distribute, Yet Things Multiply

Answer

The distributive property states that a(b + c) = ab + ac. This means when multiplying a number by a sum, we can multiply the number by each term in the sum separately and then add the results.

Answer

If both a and b are increased by 1, the new product is (a+1)(b+1) = ab + a + b + 1. Therefore, the increase is a + b + 1.

Answer

(a + m)(b + n) = ab + an + bm + mn. This is Identity 1, which shows the product is the sum of all possible products between terms of each bracket.

Answer

To multiply by 11: Write the original number, then add adjacent digits from right to left. For example, 3874 × 11: Write 3, then 3+8=11 (write 1, carry 1), then 8+7+1=16 (write 6, carry 1), then 7+4+1

Answer

Identity 1A: (a + b)² = a² + 2ab + b². This is used to find the square of a sum of two numbers. It's called the 'square of sum' identity.

Answer

Identity 1B: (a - b)² = a² - 2ab + b². This is used to find the square of a difference of two numbers. It's called the 'square of difference' identity.

Answer

Identity 1C: (a + b)(a - b) = a² - b². This is used to find the product of sum and difference of the same two numbers. It's called the 'difference of squares' identity.

Answer

104² = (100 + 4)² = 100² + 2(100)(4) + 4² = 10000 + 800 + 16 = 10816