Simplify the expression.
EXAMPLE 3
Simplify each expression by combining like terms.
a. 7x − 3x
b. 10y2 + y2
c. 8x2 + 2x − 3x
d. 8x2 + 2x − 3x
Solution
a. 7x − 3x = (7 − 3)x = 4x
b. 10y2 + y2 = 10y2 + 1y2 = (10 + 1)y2 = 11y2
c. 8x2 + 2x − 3x = 8x2 + (2 − 3)x = 8x2 − x
d. 9n2 − 5n2 + n2 = 19 − 5 + 12n2 = 5n2
EXAMPLE 4
Simplify each expression by combining like terms.
a. 2x + 3x + 5 + 2
b. −5a − 3 + a + 2
c. 4y − 3y2
d. 2.3x + 5x − 6
e.
Solution
a.
b.
c. 4y − 3y2 These two terms cannot be combined because they are unlike terms.
d.
e.
EXAMPLE 5
Find each product by using the distributive property to remove parentheses.
a. 5(3x + 2)
b. −21y + 0.3z − 12
c. − (9x + y − 2z + 6)
Solution
a.
b.
c.
EXAMPLE 6
Simplify each expression.
a. 3(2x − 5) + 1
b. −2(4x + 7) − (3x − 1)
c. 9 + 3(4x − 10)
Solution
a.
b.
c.
EXAMPLE 7
Write the phrase below as an algebraic expression. Then simplify if possible.
“Subtract 4x − 2 from 2x − 3.”
Solution
“Subtract 4x − 2 from 2x − 3” translates to 12x − 32 − 14x − 22. Next, simplify the algebraic expression.
8y − 2 − 3(y + 4)
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