PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoLet us expand some of the cubic terms using their identities.
1. (2x+3y)^3
Let us use the identity, (a+b)^3= a^3+3a^2b+3ab^2+b^3.
Comparing (2x+3y)^3 with (a+b)^3, we have a=2x and b=3y.
Substitute the values in the formula.
(2x+3y)^3 = (2x)^3+ 3(2x)^2(3y) + 3(2x)(3y)^2 + (3y)^3
(2x+3y)^3 = 8x^3+ (3 \times 4 \times 3)x^2y + (3\times 2\times 9)xy^2+ 27y^3
= 8x^3 + 36x^2y + 54xy^2 + 27y^3
2. (5x-7y)^3
Let us use the identity, (a-b)^3=a^3-3a^2b+3ab^2-b^3.
Comparing (5x-7y)^3 with (a-b)^3, we have a=5x and b=7y.
Substitute the values in the formula.
(5x-7y)^3 = (5x)^3- 3(5x)^2(7y) + 3(5x)(7y)^2 - (7y)^3
(5x-7y)^3 = 125x^3- (3\times 25\times 7)x^2y + (3\times 5 \times 49)xy^2- 343y^3
(5x-7y)^3 = 125x^3 - 525x^2y + 735xy^2 - 343y^3
Example:
Look for the following cases where we used the identities.
1. Expand (y-5)^3 using the identity.
The above expression is of the form (a-b)^3.
We have the identity, (a-b)^3=a^3-3a^2b+3ab^2-b^3.
Substitute a = y and b = 5 in the formula.
2. Evaluate 103^3 using the identity.
Rewrite 103^3 as (100+3)^3.
The above expression is of the form (a+b)^3.
We have the identity, (a+b)^3 = a^3+3a^2b+3ab^2+b^3
Substitute a =100 and b = 3 in the formula.
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