Simplify Algebraic Expressions using the Distributive Property 2

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Question 1 of 4

Simplify the expression

`8p(4q-3+p)`

Question 2 of 4

Simplify the expression

`7xy(x^2+2)`

Question 3 of 4

Simplify the expression

`3m(5m-n-2)`

	`8p``(4q-3+p)`
`=`	`(``8p``xx4q)-(``8p``xx3)+(``8p``xxp)`
`=`	`[(8xx4)xxpxxq]-[8xx3xxp]+[8xxpxxp]`	Keep the constants on the left side
`=`	`[32xxpxxq]-[24xxp]+[8xxp^(1+1)]`	Multiplication property of exponents
`=`	`32pq-24p+8p^2`	Combine the constant with the variable

	`7xy``(x^2+2)`
`=`	`(``7xy``xx x^2)+(``7xy``xx2)`
`=`	`[7xx(x^2xx x)xxy]+[(7xx2)xx x xx y]`	Keep the constants on the left side
`=`	`[7xxx^(2+1)xxy]+[14xx x xx y]`	Multiplication property of exponents
`=`	`7x^3y+14xy`	Combine the constant with the variable

	`3m``(5m-n-2)`
`=`	`(``3m``xx5m)-(``3m``xxn)-(``3m``xx2)`
`=`	`[(3xx5)xx(mxxm)]-[3xxmxxn]-[3xx2xxm]`	Keep the constants on the left side
`=`	`[15xxm^(1+1)]-[3xxmxxn]-[6xxm]`	Multiplication property of exponents
`=`	`15m^2-3mn-6m`	Remove multiplication signs

`12y` `-20+``2y`	`=`	`(``12y+2y``)-4`
	`=`	`14y` `-4`