Respuesta :

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c(x)=4x-2       and d(x)=[tex] x^{2} +5x[/tex]
(c*d)(x)
(4x-2)([tex] x^{2} +5x)[/tex]
Open the brackets and multiply the terms in the order shown below;
4x([tex] x^{2} +5x)[/tex]-2([tex] x^{2} +5x)[/tex]
=4[tex] x^{3} +20 x^{2} -2 x^{2} -10x[/tex]
=4[tex] x^{3} +18 x^{2} -10x[/tex]

The value of (c*d)(x) is 4x³ + 18x² - 10x

How to find the value of (c*d)(x)?

Given that,

  • c(x) = 4x – 2
  • d(x) = [tex]x^{2} +5x[/tex]

∴ (c*d)(x) = c(x)d(x) = (4x – 2)([tex]x^{2} +5x[/tex])

How to multiply two algebric expressions?

  • To multiply two algebric expressions, we can do it seperately term by term.
  • Then we should adjust the like terms.

∴ (4x – 2)([tex]x^{2} +5x[/tex])

= (4x)([tex]x^{2} +5x[/tex]) -2([tex]x^{2} +5x[/tex])

= 4x³ + 20x² - 2x² - 10x

= 4x³ + 18x² - 10x

∴ The value of (c*d)(x) is 4x³ + 18x² - 10x

Learn more about algebric multiplications here: https://brainly.com/question/2241589

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