Distribute • Watch the signs • Combine like terms
Distribute to every term
Multiply the outside number by every term inside the parentheses, including the negative ones.
$$3(x-4)+5x=3x-12+5x$$
Combine like terms.
$$8x-12$$
A minus distributes too
A negative outside, or a minus in front of parentheses, changes the sign of every term inside.
$$2(x-1)-3(x+4)=2x-2-3x-12$$
Combine like terms.
$$-x-14$$
Nested parentheses
Work inside first. Distribute the inner grouping, then the outer one.
$$5-3[x-7(2x-6)]=5-3[x-14x+42]$$
$$5-3x+42x-126$$
Combine like terms.
$$39x-121$$
One set of parentheses. Distribute, then combine like terms.
Simplify. \( 5(x-3)+2x \)
\(5x-15+2x\)
Combine like terms.
Answer: \(7x-15\)
Simplify. \( -3(x-4)+2 \)
\(-3x+12+2\)
Combine like terms.
Answer: \(-3x+14\)
Work inside the grouping first. Distribute both positive and negative terms, then combine like terms.
Simplify. \( 4-2[x-6(2x-3)] \)
\(4-2[x-12x+18]\)
\(4-2x+24x-36\)
Combine like terms.
Answer: \(22x-32\)
Simplify. \( 3(x+4)-2(3x-5) \)
\(3x+12-6x+10\)
Combine like terms.
Answer: \(-3x+22\)
Simplify. \( 6+4[x-3(2x-5)] \)
\(6+4[x-6x+15]\)
\(6+4x-24x+60\)
Combine like terms.
Answer: \(-20x+66\)
Simplify. \( 8-5[x+2(3x-4)] \)
\(8-5[x+6x-8]\)
\(8-5x-30x+40\)
Combine like terms.
Answer: \(-35x+48\)
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