Respuesta :
The product is 6p⁷ - 2p⁵ - 12⁶ + 4p⁴.
We are provided with expressions in three brackets. Performing multiplication between first two brackets first. This will be followed by multiplication of the product of first two brackets with the expression of third bracket.
For multiplication, the rule of exponents to be used is -
aᵇ×aⁿ = aᵇ⁺ⁿ
Rewriting the expression
Product = (p³)(2p² - 4p) (3p² - 1)
Performing multiplication of first two brackets -
Product = (p³ × 2p² - p³ × 4p) (3p² - 1)
Product = (2p⁵ - 4p⁴) (3p² - 1)
Further performing multiplication of product with third bracket -
Product = (2p⁵ × 3p² - 2p⁵ × 1 - 4p⁴ × 3p² - 4p⁴ × - 1)
Product = 6p⁷ - 2p⁵ - 12⁶ + 4p⁴
Hence, the product of given expressions is 6p⁷ - 2p⁵ - 12⁶ + 4p⁴.
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