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How do you multiply #(2t + 3)(3t - 5)#?

Answer 1

Hazel Anglin

#6t^2-t-15#

#"each term in the second bracket is multiplied by each"# #"term in the first bracket"#

#rArr(color(red)(2t+3))(3t-5)#

#=color(red)(2t)(3t-5)color(red)(+3)(3t-5)larrcolor(blue)"distribute"#

#=(color(red)(2t)xx3t)+(color(red)(2t)xx-5)+(color(red)(3)xx3t)+(color(red)(3)xx-5)#

#=6t^2color(magenta)(-10t)color(magenta)(+9t)-15larrcolor(blue)"collect like terms"#

#=6t^2-t-15#

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Answer 2

Isaiah Anthony

To multiply the expressions ((2t + 3)) and ((3t - 5)), you can use the distributive property or the FOIL method. Here's how:

Using the distributive property: [ (2t + 3)(3t - 5) = 2t \cdot 3t + 2t \cdot (-5) + 3 \cdot 3t + 3 \cdot (-5) ]

Simplify each term: [ = 6t^2 - 10t + 9t - 15 ]

Combine like terms: [ = 6t^2 - t - 15 ]

Using the FOIL method: [ (2t + 3)(3t - 5) = (2t \cdot 3t) + (2t \cdot (-5)) + (3 \cdot 3t) + (3 \cdot (-5)) ]

Simplify each term: [ = 6t^2 - 10t + 9t - 15 ]

Combine like terms: [ = 6t^2 - t - 15 ]

So, ((2t + 3)(3t - 5) = 6t^2 - t - 15).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.