What is | (x^{2} + y^{2})(x – y) – (x –y)^{3} | equal to? |
x^{2}y – xy^{2} |
(x^{2} + y^{2})(x – y) – (x –y)^{3} | ||
x^{2}y – xy^{2} |
= | (x^{3} + xy^{2} – x^{2}y – y^{3} – (x^{3} – y^{3} – 3x^{2}y + 3xy^{2}) | |
x^{2}y – xy^{2} |
= | (x^{3} + xy^{2} – x^{2}y – y^{3} – x^{3} + y^{3} + 3x^{2}y – 3xy^{2}) | |
x^{2}y – xy^{2} |
= | 2x^{2}y – 2xy^{2} | = | 2(x^{2}y – 2xy^{2}) | = 2 |
x^{2}y – xy^{2} | x^{2}y – xy^{2} |
If | ( | x^{2} + | 1 | ) | = | 17 | , then what is | ( | x^{3} – | 1 | ) | equal to? | |
x^{2} | 4 | x^{3} |
( | x^{2} + | 1 | ) | = | 17 |
x^{2} | 4 |
⇒ x^{2} + | 1 | + 2 – 2 = | 17 | ⇒ | ( | x – | 1 | ) | ^{2} | + 2 = | 17 |
x^{2} | 4 | x | 4 |
⇒ | ( | x – | 1 | ) | ^{2} | = | 17 | – 2 ⇒ | ( | x – | 1 | ) | ^{2} | = | 9 |
x | 4 | x | 4 |
⇒ | ( | x – | 1 | ) | = | 3 |
x | 2 |
⇒ | ( | x – | 1 | ) | ^{3} | = | ( | 3 | ) | ^{3} |
x | 2 |
⇒ x^{3} – | 1 | – 3 × | 1 | .x | ( | x – | 1 | ) | = | 27 | |
x^{3} | x | x | 8 |
⇒ x^{3} – | 1 | = | 27 | + 3 × | ( | 3 | ) |
x^{3} | 8 | 2 |
⇒ x^{3} – | 1 | = | 27 | + | 9 |
x^{3} | 8 | 2 |
⇒ | ( | x^{3} – | 1 | ) | = | 63 | |
x^{3} | 8 |