Expand the expression : (a) (x^(2)-2)(x^(2)+6)

Apply Distributive Property: Apply the distributive property (also known as the FOIL method for binomials) to multiply the two expressions. (x^(2)-2)(x^(2)+6) = x^(2) * x^(2) + x^(2) * 6 - 2 * x^(2) - 2 * 6Perform Multiplication: Perform the multiplication for each term. x^(2) * x^(2) = x^(4) x^(2) * 6 = 6x^(2) -2 * x^(2) = -2x^(2) -2 * 6 = -12Combine Like Terms: Combine like terms. x^(4) + 6x^(2) - 2x^(2) - 12 x^(4) + (6x^(2) - 2x^(2)) - 12 x^(4) + 4x^(2) - 12Write Final Expression: Write the final simplified expression. The product of the expressions (x^(2)-2) and (x^(2)+6) is x^(4) + 4x^(2) - 12.

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Expand the expression : (a)
(x^(2)-2)(x^(2)+6)

Expand the expression : (a) $\left(x^{2}-2\right)\left(x^{2}+6\right)$

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Algebra 1

Evaluate integers raised to rational exponents

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Q. Expand the expression : (a)

\left(x^{2}-2\right)\left(x^{2}+6\right)

Apply Distributive Property: Apply the distributive property (also known as the FOIL method for binomials) to multiply the two expressions. $\newline$ $(x^{2}-2)(x^{2}+6) = x^{2} \times x^{2} + x^{2} \times 6 - 2 \times x^{2} - 2 \times 6$
Perform Multiplication: Perform the multiplication for each term. $\newline$ $x^{2} \times x^{2} = x^{4}$ $\newline$ $x^{2} \times 6 = 6x^{2}$ $\newline$ $-2 \times x^{2} = -2x^{2}$ $\newline$ $-2 \times 6 = -12$
Combine Like Terms: Combine like terms. $\newline$ $x^{4} + 6x^{2} - 2x^{2} - 12$ $\newline$ $x^{4} + (6x^{2} - 2x^{2}) - 12$ $\newline$ $x^{4} + 4x^{2} - 12$
Write Final Expression: Write the final simplified expression. $\newline$ The product of the expressions $x^{2}-2$ and $x^{2}+6$ is $x^{4} + 4x^{2} - 12$ .