Question

Help: Write as a polynomial: 7b(4c - b) + 4c(c - 7b)

Answer 1

To write the expression 7b(4c - b) + 4c(c - 7b) as a polynomial, distribute the terms in the parentheses and combine like terms to get the simplified polynomial 4c² - 7b².

Step-by-step explanation:

The question asks to write the expression 7b(4c - b) + 4c(c - 7b) as a polynomial. To do this, you must distribute the terms inside the parentheses and then combine like terms. Here's a step-by-step solution:

1. Distribute 7b across (4c - b): 7b × 4c gives 28bc, and 7b × -b gives -7b². So we have 28bc - 7b².
2. Distribute 4c across (c - 7b): 4c × c gives 4c², and 4c × -7b gives -28bc. So we have 4c² - 28bc.
3. Add the distributed terms together: 28bc - 7b² + 4c² - 28bc. The 28bc and -28bc terms cancel each other out.
4. The resulting polynomial is 4c² - 7b².