Combining Like Terms 3
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Question 1 of 4
1. Question
Simplify`p^2+pq+3qp+q^2`Hint
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When simplifying expressions, like terms can be combined or operated on.The variable `qp` can also be written as `pq`, and can be combined to another similar term.Note that variables without constants have `1` as a constant.`=` `p^2+``pq` `+3qp+q^2` `p^2+``pq` `+3``pq` `+q^2` `qp=pq` `=` `p^2+(1+3)``pq` `+q^2` Solve the constants of like terms `=` `p^2+q^2+4pq` Rearrange the values further `p^2+q^2+4pq` -
Question 2 of 4
2. Question
Simplify`6n+5(3n+8)`- (21n+40)
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When simplifying expressions, like terms can be combined or operated on.Start by distributing `5` so that we will have all terms separated.`6n+5(3n+8)` `=` `6n+(5xx3n)+(5xx8)` `=` `6n+15n+40` Since there are two terms that both have the variable `n`, we can combine them.`6``n` `+15``n` `+40` `=` `(6+15)``n` `+40` Solve the constants of like terms `=` `21n+40` `21n+40` -
Question 3 of 4
3. Question
Simplify`(x+3)-(x-y)`- (y+3)
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When simplifying expressions, like terms can be combined or operated on.Start by distributing `-1` to the second parenthesis so that we will have all terms separated.`(x+3)-(x-y)` `=` $$x+3+[ (-1) \times x ]-[ (-1) \times y ]$$ `=` `x+3-x+y` Since there are two terms that both have the variable `x`, we can combine them.Note that variables without constants have `1` as a constant.`x` `+3-``x` `+y` `=` `(1-1)``x` `+3+y` Solve the constants of like terms `=` `(0)``x` `+3+y` `=` `0+3+y` `0` multiplied to any number equals `0` `=` `y+3` Rearrange the values further `y+3` -
Question 4 of 4
4. Question
Simplify`4(x+2y)+3(5x-y)`- (19x+5y)
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When simplifying expressions, like terms can be combined or operated on.Start by distributing `4` and `3` to their respective parentheses so that we will have all terms separated.`4(x+2y)+3(5x-y)` `=` `(4xx x)+(4xx2y)+(3xx5x)-(3xxy)` `=` `4x+8y+15x-3y` Since there are two terms that both have the variable `x`, we can combine them.`4``x` `+8y+15``x` `-3y` `=` `(4+15)``x` `+8y-3y` Solve the constants of like terms `=` `19x+8y-3y` There are also two terms that both have the variable `y`, so we can combine them.`19x+8``y` `-3``y` `=` `19x+(8-3)``y` Solve the constants of like terms `=` `19x+5y` `19x+5y`
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