I need to solve the distributive property for -3x4{ 4x-5y+2}

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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Supposing that the multiplication you need to perform is `-3*x^4*(4x - 5y + 2)` , using the distributive property of multiplication over addition, yields:

`-3*x^4*(4x - 5y + 2) = -3*x^4*(4x) -3*x^4*(-5y) + (-3*x^4)*2`

You need to use the following property of powers, such that:

`x^a*x^b = x^(a+b)`

Reasoning by analogy, yields:

`x^4*x^3 = x^(4+3) => x^4*x^3 = x^7`

`-3*x^4*(4x - 5y + 2) = (-3*4)*x^7 + (-3*(-5))*x^4*y) + (-3*2)*x^4`

Notice that the property of powers holds for powers having like bases.

`-3*x^4*(4x - 5y + 2) = -12x^7 + 15x^4*y - 6x^4`

Hence, performing the multiplication using not only the distributive property of multiplication over addition, butalso the property of powers having like bases and the rule of signs, yields `-3*x^4*(4x - 5y + 2) = -12x^7 + 15x^4*y - 6x^4.`

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