(x%5E2%2B3)-(3%2Bx%5E2)%5E3.jpeg "(x^4-3x^2+9)(x^2+3)-(3+x^2)^3")
Simplifying the Expression: (x^4-3x^2+9)(x^2+3)-(3+x^2)^3
This article will guide you through simplifying the algebraic expression: (x^4-3x^2+9)(x^2+3)-(3+x^2)^3.
Step 1: Expanding the First Term
We begin by expanding the first term using the distributive property:
(x^4-3x^2+9)(x^2+3) = x^4(x^2+3) - 3x^2(x^2+3) + 9(x^2+3)
Expanding further:
= x^6 + 3x^4 - 3x^4 - 9x^2 + 9x^2 + 27
This simplifies to: x^6 + 27
Step 2: Expanding the Second Term
We now expand the second term using the cube of a binomial formula:
(3+x^2)^3 = 3^3 + 3(3^2)(x^2) + 3(3)(x^2)^2 + (x^2)^3
Expanding further:
= 27 + 27x^2 + 9x^4 + x^6
Step 3: Combining the Expanded Terms
Now we can combine the results from step 1 and step 2:
(x^4-3x^2+9)(x^2+3)-(3+x^2)^3 = (x^6 + 27) - (27 + 27x^2 + 9x^4 + x^6)
Step 4: Simplifying the Expression
Finally, we simplify the expression by combining like terms:
= x^6 + 27 - 27 - 27x^2 - 9x^4 - x^6
= -9x^4 - 27x^2
Therefore, the simplified form of the given expression is -9x^4 - 27x^2.