Ms. Peterson wrote the expression below on the chalkboard for her class. She asked the students to write an equivalent expression using no more than one

set of parentheses. 4 (3x+5y+2z) + 3 (x-z) • Tom wrote 12x+20y+8z • Jenna wrote 5 (3x+4y+z) • Chris wrote 15x+20y-5zWhich, if any, of the three students wrote an expression that is equivalent to Ms. Peterson's expression?

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Mathematics

6 April, 14:43

Ms. Peterson wrote the expression below on the chalkboard for her class. She asked the students to write an equivalent expression using no more than one

set of parentheses. 4 (3x+5y+2z) + 3 (x-z) • Tom wrote 12x+20y+8z • Jenna wrote 5 (3x+4y+z) • Chris wrote 15x+20y-5zWhich, if any, of the three students wrote an expression that is equivalent to Ms. Peterson's expression?

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Randy Crosby · Answer 1

So first we solve

4 (3x+5y+2z) + 2 (x-z)

fist we distribute

4 times 3x=12x

4 times 5y=20y

4 times 2z=8z

12x+20y+8z

then the second part

3 (x-z)

3 times x=3x

3 times - z=-3z

3x-3z

combine

12x+20y+8z+3x-3z

group like terms

15x+20y+5z

so

tom:12x+20y+8z

this is only the first part so he is wrong

Jenna:5 (3x+4y+z)

this is correct beccause if we multiply it we get

15x+20y+5z which is correct

chris: 15x+20y+5z is correct

Jenna and Chris are correct