Question

if a=0 and b=1, find the value of
1. a³+b³+3a²b+3ab²
2. a²+2ab+b²
3. a²-b²
4. (a+b)(a-b)
5. (a+b)³
6. (a+b)²


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Answer 1

✪ Question ✪

If a=0 and b=1, find the value of

1. a³+b³+3a²b+3ab²

2. a²+2ab+b²

3. a²-b²

4. (a+b)(a-b)

5. (a+b)³

6. (a+b)²

✪ Given ✪

• a = 0
• b = 1

✪ To find ✪

The values.

✪ Formulae to be used ✪

a³+b³+3a²b+3ab² = (a+b)³

a²+2ab+b² = (a+b)²

a²-b² = (a+b)(a-b)

✪ Solution ✪

1. a³+b³+3a²b+3ab²

a³+b³+3a²b+3ab²

= (a+b)³

= (0+1)³

= 1³

= 1

2. a²+2ab+b²

a²+2ab+b²

= (a+b)²

= (0+1)²

= 1²

= 1

3. a²-b²

a²-b²

= 0²-1²

= 0-1

= -1

4. (a+b)(a-b)

(a+b)(a-b)

= a²-b²

= 0²-1²

= 0-1

= -1

5. (a+b)³

(a+b)³

= (0+1)³

= 1³

= 1

6. (a+b)²

(a+b)²

= (0+1)²

= 1²

= 1

✪ Hence ✪

When a = 0 and b = 1,

• a³+b³+3a²b+3ab² = 1
• a²+2ab+b² = 1
• a²-b² = -1
• (a+b)(a-b) = -1
• (a+b)³ = 1
• (a+b)² = 1

________________________________

✪ Some more formulae ✪

☞ (a+b)² = a²+2ab+b²

☞ (a-b)² = a²-2ab+b²

☞ a²-b² = (a+b)(a-b)

☞ a²+b² = (a+b)²-2ab

☞ a²+b² = (a-b)²+2ab

☞ 2(a²+b²) = (a+b)²+(a-b)²

☞ (a+b)³ = a³+3a²b+3ab²+b³

☞ (a-b)³ = a³-3a²b+3ab²-b³

☞ a³+b³ = (a+b)(a²-ab+b²)

☞ a³-b³ = (a-b)(a²+ab+b²)

     ๑ Hope this helps you. ๑