Answer:
1a (x + y)² = x² + 2xy + y²
1b. (x - y)² = x² - 2xy + y²
2. (x + y)² - (x - y)² = 4xy
3. 4² – 2² = 12
Explanation:
1a. Expansion of (x + y)²
(x + y)² = (x + y)(x + y)
(x + y)² = x(x + y) + y(x + y)
(x + y)² = x² + xy + xy + y²
(x + y)² = x² + 2xy + y²
1b. Expansion of (x - y)²
(x - y)² = (x - y)(x - y)
(x - y)² = x(x - y) - y(x - y)
(x - y)² = x² - xy - xy + y²
(x - y)² = x² - 2xy + y²
2. Determination of (x + y)² - (x - y)²
This can be obtained as follow
(x + y)² = x² + 2xy + y²
(x - y)² = x² - 2xy + y²
(x + y)² - (x - y)² = x² + 2xy + y² - (x² - 2xy + y²)
= x² + 2xy + y² - x² + 2xy - y²
= x² - x² + 2xy + 2xy + y² - y²
= 2xy + 2xy
= 4xy
(x + y)² - (x - y)² = 4xy
3. Writing 12 as the difference of two perfect square.
To do this, we shall subtract 12 from a perfect square to obtain a number which has a perfect square root.
We'll begin by 4
4² – 12
16 – 12 = 4
Find the square root of 4
√4 = 2
4 has a square root of 2.
Thus,
4² – 12 = 4
4² – 12 = 2²
Rearrange
4² – 2² = 12
Therefore, 12 as a difference of two perfect square is 4² – 2²