Final answer:
Clare's claims are incorrect. (10+3)(10-3) equals 91, not 1032, and (20+1)(20-1) equals 399, not 202-12, because these are instances of the difference of squares formula in algebra.
Step-by-step explanation:
No, I do not agree with Clare's claims. The expressions (10+3)(10-3) and (20+1)(20-1) are examples of the difference of squares, which is aspecial product in algebra. The difference of squares formula states that for any two numbers a and b, the equation (a+b)(a-b) is equal to a² - b².
For the first claim, using the difference of squares formula, we calculate (10+3)(10-3) as 10² - 3², which equals 100 - 9 = 91, not the claimed 10³². For the second claim, (20+1)(20-1) should be calculated as 20² - 1², which equals 400 - 1 = 399, not the claimed 20²-1². Therefore, Clare's claims are incorrect.
In summary, here's how we can correct the misconceptions:
- (10 + 3)(10 - 3) = 10² - 3² = 100 - 9 = 91
- (20+1)(20-1) = 20² - 1² = 400 - 1 = 399
Remember, when performing such multiplications, you should square each term separately and then subtract the second square from the first.