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Clare claims that (10+3)(10-3) is equivalent to 10 32 and and (20+1)(20-1) is equivalent to 202-12 Do you agree?

a. Yes
b. No

User KellCOMnet
by
7.9k points

1 Answer

6 votes

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.

User Michael Mikhjian
by
8.7k points
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