Question

Simplify the expression (4x3)2 + x3 (x3+2x) +3x4.

Answer 1

(4x3)2+3x(3x+2x)+3x+4

24x+15x²+3x+4

15x²+27x+4

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Answer 2

The simplified expression is $16x^6 + x^6+2x^4 +3x^4$.

Explanation:

The given expression : $(4x^3)^2 + x^3 (x^3+2x) +3x^4.$   (*)

To simplify the given expression , we use exponential property for first term

$(a^m)^n=a^{mn}$   (1)

Then ,the first term will become: $(4x^3)^2 =(4)^2(x^3)^2= 16x^{3\times2}=16x^6$         (i)

For second term we first use distributive property: $a(b+c)=ab+ac$$x^3 (x^3+2x) = x^3\cdot x^3+x^3\cdot 2x$

Now use exponential property $a^m\times a^n=a^{m+n}$

we get

$x^{3+3}+2x^{3+1}$

$=x^6+2x^4$         (ii)

Third term is already simplified.

Now replace the simplified terms from (i) and (ii) in (*) , we get

$16x^6 + x^6+2x^4 +3x^4$

Hence, the simplified expression is $16x^6 + x^6+2x^4 +3x^4$.

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