Use long division :
(a^3-b^3)/ (a-b)
Go on calc 101 dot com
When page be open click option :
long division
See the difference of two cubes, you should memorize this.
(a^3-b^3)= (a-b)(a^2+ab+b^2)
To solve the expression: (a^3 - b^3) / (a - b) using long division, follow these steps:
Step 1: Write the expression in long division form
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a - b | a^3 - b^3
Step 2: First, divide the first term of the dividend (a^3) by the divisor (a - b), which gives you (a^2).
a^2
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a - b | a^3 - b^3
Step 3: Multiply the divisor (a - b) by the quotient you just got (a^2), and write the result (a^3 - a^2b) below the dividend term (a^3 - b^3).
a^2
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a - b | a^3 - b^3
- (a^3 - a^2b)
Step 4: Subtract the result in Step 3 from the dividend. In this case, subtract (a^3 - a^2b) from (a^3 - b^3). The result is (-a^2b + b^3).
a^2
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a - b | a^3 - b^3
- (a^3 - a^2b)
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-a^2b + b^3
Step 5: Bring down the next term of the dividend (-a^2b + b^3), which is b^3.
a^2 + _____
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a - b | a^3 - b^3
- (a^3 - a^2b)
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-a^2b + b^3
Step 6: Divide the term you brought down (b^3) by the divisor (a - b), which gives you (-b^2).
a^2 - b^2
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a - b | a^3 - b^3
- (a^3 - a^2b)
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-a^2b + b^3
Step 7: Multiply the divisor (a - b) by the new quotient (-b^2), and write the result (-b^2a + b^3) below the dividend term (-a^2b + b^3).
a^2 - b^2
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a - b | a^3 - b^3
- (a^3 - a^2b)
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-a^2b + b^3
+ (-b^2a + b^3)
Step 8: Subtract the result in Step 7 from the previous result in Step 6. In this case, subtract (-b^2a + b^3) from (-a^2b + b^3). The result is (-a^2b + b^3 + b^2a - b^3).
a^2 - b^2
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a - b | a^3 - b^3
- (a^3 - a^2b)
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-a^2b + b^3
+ (-b^2a + b^3)
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-2a^2b
The final result after performing long division is -2a^2b.