simplify the following.
1}(4a-3)^3 -(4a+3)^3
2}(5x-7y)^3+(5x+7y)^3
Answers
Step-by-step explanation:
1} (4a - 3)³ - (4a + 3)³
using (x - y)³ = x³ - y³ - 3xy(x - y)
= (4a)³ - (3)³ - 3 × 4a × 3(4a - 3) - (4a + 3)³
= 64a³ - 27 - 36a(4a - 3) - (4a + 3)³
= 64a³ - 27 - 144a² + 108a - (4a + 3)³
= 64a³ - 144a² + 108a - 27 - (4a + 3)³
using (x + y)³ = x³ + y³ + 3xy(x + y)
= 64a³ - 144a² + 108a - 27 - (4a)³ + (3)³ + 3 ×
4a × 3(4a + 3)
= 64a³ - 144a² + 108a - 27 - 64a³ + 27 + 36a(4a +
3)
= 64a³ - 144a² + 108a - 27 - 64a³ + 27 + 144a² +
108a
= 64a³ - 144a² + 108a - 27 - 64a³ + 144a² + 108a +
27
= 64a³ - 64a³ - 144a² + 114a² + 108a + 108a + 27 -
27
= 216a
2} (5x - 7y)³ + (5x + 7y)³
= using (x - y)³ = x³ - y³- 3xy(x - y)
= (5x)³ - (7y)³ - 3 × 5x × 7y(5x - 7y) + (5x + 7y)³
= 125x³ - 343y³ - 105xy(5x - 7y) + (5x + 7y)³
= 125x³ - 343y³ - 525x²y - 735xy² + (5x + 7y)³
= 125x³ - 525x²y + 735xy² - 343y³ + (5x + 7y)³
using (x + y)³ = x³ + y³ + 3xy(x + y)
= 125x³ - 525x²y + 735xy² - 343y³ + (5x)³ + (7y)³ +
3 × 5x × 7y(5x + 7y)
= 125x³ - 525x²y + 735xy² - 343y³ + 125x³ + 343y³
+ 105xy(5x + 7y)
= 125x³ - 525x²y + 735xy² - 343y³ + 125x³ + 343y³
+ 525x²y + 735xy²
= 125x³ - 525x²y + 735xy² - 343y³ + 125x³ +
525x²y + 735xy² + 343y³
= 250x³ + 1470y²
Answer:
1} (4a - 3)³ - (4a + 3)³
using (x - y)³ = x³ - y³ - 3xy(x - y)
= (4a)³ - (3)³ - 3 × 4a × 3(4a - 3) - (4a + 3)³
= 64a³ - 27 - 36a(4a - 3) - (4a + 3)³
= 64a³ - 27 - 144a² + 108a - (4a + 3)³
= 64a³ - 144a² + 108a - 27 - (4a + 3)³
using (x + y)³ = x³ + y³ + 3xy(x + y)
= 64a³ - 144a² + 108a - 27 - (4a)³ + (3)³ + 3 ×
4a × 3(4a + 3)
= 64a³ - 144a² + 108a - 27 - 64a³ + 27 + 36a(4a +
3)
= 64a³ - 144a² + 108a - 27 - 64a³ + 27 + 144a² +
108a
= 64a³ - 144a² + 108a - 27 - 64a³ + 144a² + 108a +
27
= 64a³ - 64a³ - 144a² + 114a² + 108a + 108a + 27 -
27
= 216a
2} (5x - 7y)³ + (5x + 7y)³
= using (x - y)³ = x³ - y³- 3xy(x - y)
= (5x)³ - (7y)³ - 3 × 5x × 7y(5x - 7y) + (5x + 7y)³
= 125x³ - 343y³ - 105xy(5x - 7y) + (5x + 7y)³
= 125x³ - 343y³ - 525x²y - 735xy² + (5x + 7y)³
= 125x³ - 525x²y + 735xy² - 343y³ + (5x + 7y)³
using (x + y)³ = x³ + y³ + 3xy(x + y)
= 125x³ - 525x²y + 735xy² - 343y³ + (5x)³ + (7y)³ +
3 × 5x × 7y(5x + 7y)
= 125x³ - 525x²y + 735xy² - 343y³ + 125x³ + 343y³
+ 105xy(5x + 7y)
= 125x³ - 525x²y + 735xy² - 343y³ + 125x³ + 343y³
+ 525x²y + 735xy²
= 125x³ - 525x²y + 735xy² - 343y³ + 125x³ +
525x²y + 735xy² + 343y³
= 250x³ + 1470y²
Step-by-step explanation: