Question

write the following cubes in the expanded form 1. (107)cube 2.(96)cube​

Answer 1

Answer:

use identity in this question

Answer 2

1. 12,25,043
2. 8,84,736

Step-by-step explanation:

1. 107^(3)

• Using identity {a^(3) + b^(3)} = a^(3) + b^(3) + 3a^(2)b + 3ab^(2)
• 107^(3) can be written in the form {100^(3) + 7^(3)}
• So,

{100^(3) + 7^(3)} = 100^(3) + 7^(3) + [3 × {100^(2)} × 7] + [3 × 100 × {7^(2)}

• 10,00,000 + 343 + 2,10,000 + 14,700
• (10,00,000 + 343) + (2,10,000 + 14,700)
• 10,00,343 + 2,24,700
• 12,25,043

2. 96^(3)

• Using identity {a^(3) + b^(3)} = a^(3) + b^(3) + 3a^(2)b + 3ab^(2)
• 96^(3) can be written in the form {90^(3) + 6^(3)}
• So,

{90^(3) + 6^(3)} = 90^(3) + 6^(3) + [3 × {90^(2)} × 6] + [3 × 90 × {6^(2)}

• 7,29,000 + 216 + 1,45,800 + 9,720
• (7,29,000 + 216) + (1,45,800 + 9,720)
• 7,29,216 + 1,55,520
• 8,84,736