Adding Variables With Exponents

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Exponent is also known as index or power. If a number “x” is multiplied n times i.e., x * x * x * x* … n times then instead of writing like this we can just simply write as x^n (read as x to the power n) where n is the power of base x.

For example suppose 2 is multiplied 6 times which means 2 * 2 * 2 * 2 * 2 *2 or we can simply represent this as 2^6 which is equal to 64.
 

Examples of adding variables with exponents: -
 
Simplify: -
1)    6^2 + 5^3
2)    x^3 + 2x^2 + x
3)    (x^2 + 5x + 6) + (3x^2 + 2) + x^3 (1 + x)
4)    (x+3)^3 + (x-2)^2
 

Solution: -

1)    6^2 + 5^3 = 36 + 125 =161
2)    x^3 + 2x^2 + x   = x(x^2 + 2x + 1)
= x (x + 1)^2
3)    (x^2 + 5x + 6) + (3x^2 + 2) + x^3 (1 + x)
=x^2 +5x + 6 + 3x^2 + 2 + x^3 + x^4
=x^4 + x^3 + (x^2 + 3x^2) +5x + (6 + 2)
= x^4 + x^3 + 4x^2 + 5x + 8
4)    (x+3)^3 + (x-2)^3
=x^3 + 3* x^2 * 3 + 3 * x * 3^2 + 3^3 + x^3 – 3 * x^2 * 2 + 3 * x * 2^2 -2^3
=x^3 + 9x^2 + 27x + 27+x^3-6x^2+12x-8
=2x^3 + 3x^2 + 39x+ 19
 




 

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