When expanding the brackets (2a-3b)²
When expanding (2a-3b)², we use the formula:
(a-b)² = a² - 2ab + b²
So, substituting 2a for a and -3b for b, we get:
(2a-3b)² = (2a)² - 2(2a)(-3b) + (-3b)²
= 4a² + 12ab + 9b²
Therefore, (2a-3b)² expands to 4a² + 12ab + 9b².
4a² + 12ab + 9b²
where is the minus sign ?
4a² - 12ab + 9b²
Apologies for the error in the previous answer. The correct expansion of (2a-3b)² is:
(2a-3b)² = (2a)² - 2(2a)(3b) + (-3b)²
= 4a² - 12ab + 9b²
So, the expansion of (2a-3b)² is 4a² - 12ab + 9b², with a negative sign between the second and third terms.
To expand the brackets (2a - 3b)², you can use the formula for expanding a binomial squared, which is (a - b)² = a² - 2ab + b².
In this case, we have (2a - 3b)². So we can substitute "a" with "2a" and "b" with "-3b" in the formula.
Now let's expand it step by step:
Step 1: Square the first term, which is (2a)². This gives us 4a².
Step 2: Multiply the first term, 2a, by the second term, -3b. This gives us -6ab.
Step 3: Multiply the second term, -3b, by the first term, 2a. This also gives us -6ab.
Step 4: Square the second term, which is (-3b)². This gives us 9b².
Putting it all together, we have:
(2a - 3b)² = 4a² - 6ab - 6ab + 9b²
Now we can simplify:
= 4a² - 12ab + 9b²
So, the expansion of (2a - 3b)² is 4a² - 12ab + 9b².