Explanation: The problems in this problem set look like (x + 4)² which can be listed as 2 binomials, side by side, to look like this (x + 4)(x + 4). The term 'x' in the first binomial is multiplied by the 'x' and the 4 in the second binomial to become x² + 4x. The '4' in the first binomial is multiplied by the 'x' and the 4 in the second binomial to become 4x + 16. Now the 4 terms of the products are combined, x² + 4x + 4x + 16. The middle two terms combine and the answer becomes x² + 8x + 16. Notice when you square a binomial such as (x + 4)² the 1st term of the answer is the square of the 1st term of the binomial, the last term in the answer is the square of the 2nd of the binomial. The middle term is twice the product of the 2 terms of the binomial. The pattern is shown as (a + b)² = a² + 2ab + b².
(x + 9)² = x * x + x * 9 + x * 9 + 9 * 9 which becomes x² + 18x + 81
(4 + x)² = 4 * 4 + 4 * x + 4 * x + x * x which becomes 16 + 8x + x²
Directions: For each problem in this problem set you may multiply terms and then combine 2 of the terms or simply follow the pattern to accomplish the final answer in one step. Strive for being able to accomplish the problems with ease and then strive for increasing your speed. Good luck and enjoy the challenge!