[2a + 3b] [2a - 3b. May you please explain the steps if you can.
multiply everything out, then add like terms
(2a+3b)(2a-3b) = 2a^2 +6ba -6ab - 9b^2 = 2a^2 - 9b^2
Thanks Jennifer!!!!!
Certainly! To simplify the expression [2a + 3b] [2a - 3b], we can use the distributive property of multiplication. This property states that when we multiply a sum by another number, we need to distribute the multiplication to each term inside the parentheses.
Let's go step-by-step:
Step 1: Start by multiplying the first terms, which are 2a and 2a.
- (2a) * (2a) = 4a²
Step 2: Next, multiply the first term of the first expression by the second term of the second expression and vice versa.
- (2a) * (-3b) = -6ab
- (3b) * (2a) = 6ab
Step 3: Multiply the second terms, which are 3b and -3b.
- (3b) * (-3b) = -9b²
Now, we can combine all the terms we obtained:
The simplified expression becomes: 4a² + (-6ab) + (6ab) + (-9b²).
The middle two terms (-6ab and 6ab) cancel each other out since they have the same value but opposite signs.
So, the final simplified expression is: 4a² - 9b².
Therefore, [2a + 3b] [2a - 3b] simplifies to 4a² - 9b².