(3b%2B4a)-(7a%2B3b)(2a%2Bb).jpeg "(2a+5b)(3b+4a)-(7a+3b)(2a+b)")
Expanding and Simplifying the Expression (2a+5b)(3b+4a)-(7a+3b)(2a+b)
This expression involves expanding two binomials and then subtracting the results. Let's break it down step by step:
Expanding the First Product: (2a+5b)(3b+4a)
We can use the FOIL method (First, Outer, Inner, Last) to expand this product:
- First: (2a)(3b) = 6ab
- Outer: (2a)(4a) = 8a²
- Inner: (5b)(3b) = 15b²
- Last: (5b)(4a) = 20ab
Combining these terms, we get: 6ab + 8a² + 15b² + 20ab
Expanding the Second Product: (7a+3b)(2a+b)
Again using the FOIL method:
- First: (7a)(2a) = 14a²
- Outer: (7a)(b) = 7ab
- Inner: (3b)(2a) = 6ab
- Last: (3b)(b) = 3b²
This simplifies to: 14a² + 7ab + 6ab + 3b²
Combining the Expanded Products
Now we have:
(6ab + 8a² + 15b² + 20ab) - (14a² + 7ab + 6ab + 3b²)
To subtract, we distribute the negative sign:
6ab + 8a² + 15b² + 20ab - 14a² - 7ab - 6ab - 3b²
Simplifying the Expression
Finally, we combine like terms:
(8a² - 14a²) + (6ab + 20ab - 7ab - 6ab) + (15b² - 3b²)
This simplifies to:
-6a² + 13ab + 12b²
Therefore, the simplified form of the expression (2a+5b)(3b+4a)-(7a+3b)(2a+b) is -6a² + 13ab + 12b².