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Exercise

$b^{12}-25$

Step-by-step Solution

1

Simplify $\sqrt{b^{12}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $12$ and $n$ equals $\frac{1}{2}$

$\left(b^{6}+\sqrt{25}\right)\left(\sqrt{b^{12}}-\sqrt{25}\right)$
2

Calculate the power $\sqrt{25}$

$\left(b^{6}+5\right)\left(\sqrt{b^{12}}-\sqrt{25}\right)$
3

Simplify $\sqrt{b^{12}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $12$ and $n$ equals $\frac{1}{2}$

$\left(b^{6}+5\right)\left(b^{6}-\sqrt{25}\right)$
4

Calculate the power $\sqrt{25}$

$\left(b^{6}+5\right)\left(b^{6}- 5\right)$
5

Multiply $-1$ times $5$

$\left(b^{6}+5\right)\left(b^{6}-5\right)$

Final answer to the exercise

$\left(b^{6}+5\right)\left(b^{6}-5\right)$

Try other ways to solve this exercise

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  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Prove from LHS (left-hand side)
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Similar Questions Solved

$x^2-121$

$a^6-3a^4+8a^3-4a^2$

$4x^2-49$

$25x^2y^4-121$

$x^2-25$

$x^2-225$

$49-x^2$

Main Topic: Factor by Difference of Squares

The difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2=(a+b)(a-b) in elementary algebra.

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