Final answer:
Two binomials whose product is x squared minus 16 are (x + 4)(x - 4).
Step-by-step explanation:
Two binomials whose product is x squared minus 16 are: (x + 4)(x - 4)
To explain this, we use the difference of squares formula which states that a^2 - b^2 = (a + b)(a - b). In this case, a = x and b = 4. To find two binomials whose product is x squared minus 16, we look for two expressions that when multiplied together result in the original expression. The given expression is a difference of squares, which can be factored into (x + 4)(x - 4). This factorization is derived from the identity a² - b² = (a + b)(a - b), where in our case, a is x, and b is 4. The binomials (x + 4) and (x - 4) are the solution because: The product of (x + 4) and (x - 4) is (x + 4)(x - 4) = x² - 4x + 4x - 16 = x² - 16. Notice the middle terms -4x and +4x cancel each other out, leaving only x² - 16.