Polynomial combining like terms (ACT/SAT). Game on.

Polynomial combining like terms (ACT/SAT) is a grade 9 math skill aligned to Common Core standard HSA.APR.A.1: understand that polynomials form a system analogous to the integers: they are closed under addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 polynomial combining like terms (act/sat) problems our math games drill.

CCSS HSA.APR.A.110 questions in the bank
Kickoff

8 plays. No signup.

Warm-upeasy

Simplify: (5x2+3x+2)−(2x2−5).(5x^2 + 3x + 2) - (2x^2 - 5)\textsf{.}

Distribute the minus sign: (5x2+3x+2)−2x2+5.(5x^2 + 3x + 2) - 2x^2 + 5\textsf{.} Combine x2x^2 terms: 5x2−2x2=3x2.5x^2 - 2x^2 = 3x^2\textsf{.} The xx term stays 3x.3x\textsf{.} Combine constants: 2+5=7.2 + 5 = 7\textsf{.} Result: 3x2+3x+7.3x^2 + 3x + 7\textsf{.}

Mid-gameeasy

Simplify: (x2+4x−5)+(2x2−4x+9).(x^2 + 4x - 5) + (2x^2 - 4x + 9)\textsf{.}

Combine x2x^2 terms: x2+2x2=3x2.x^2 + 2x^2 = 3x^2\textsf{.} The xx terms cancel: 4x−4x=0.4x - 4x = 0\textsf{.} Combine constants: −5+9=4.-5 + 9 = 4\textsf{.} Result: 3x2+4.3x^2 + 4\textsf{.}

Mid-gameeasy

Simplify: (x2+6)+(4x2−6).(x^2 + 6) + (4x^2 - 6)\textsf{.}

Combine x2x^2 terms: x2+4x2=5x2.x^2 + 4x^2 = 5x^2\textsf{.} The constants cancel: 6−6=0.6 - 6 = 0\textsf{.} Result: 5x2.5x^2\textsf{.}

Mid-gamemedium

Simplify: (4x2−x+6)−(2x2+3x−1).(4x^2 - x + 6) - (2x^2 + 3x - 1)\textsf{.}

Distribute the minus sign: (4x2−x+6)−2x2−3x+1.(4x^2 - x + 6) - 2x^2 - 3x + 1\textsf{.} Combine x2x^2 terms: 4x2−2x2=2x2.4x^2 - 2x^2 = 2x^2\textsf{.} Combine xx terms: −x−3x=−4x.-x - 3x = -4x\textsf{.} Combine constants: 6+1=7.6 + 1 = 7\textsf{.} Result: 2x2−4x+7.2x^2 - 4x + 7\textsf{.}

Mid-gamemedium

Simplify: (5x2+3)−(x2−2x).(5x^2 + 3) - (x^2 - 2x)\textsf{.}

Distribute the minus sign: (5x2+3)−x2+2x.(5x^2 + 3) - x^2 + 2x\textsf{.} Combine x2x^2 terms: 5x2−x2=4x2.5x^2 - x^2 = 4x^2\textsf{.} The xx term is 2x.2x\textsf{.} The constant stays 3.3\textsf{.} Result: 4x2+2x+3.4x^2 + 2x + 3\textsf{.}

Mid-gamemedium

Simplify: (2x2+7x+1)+(−x2+2x−4).(2x^2 + 7x + 1) + (-x^2 + 2x - 4)\textsf{.}

Combine x2x^2 terms: 2x2−x2=x2.2x^2 - x^2 = x^2\textsf{.} Combine xx terms: 7x+2x=9x.7x + 2x = 9x\textsf{.} Combine constants: 1−4=−3.1 - 4 = -3\textsf{.} Result: x2+9x−3.x^2 + 9x - 3\textsf{.}

Mid-gamemedium

Simplify: (9x2−4x)−(3x2−4x+5).(9x^2 - 4x) - (3x^2 - 4x + 5)\textsf{.}

Distribute the minus sign: (9x2−4x)−3x2+4x−5.(9x^2 - 4x) - 3x^2 + 4x - 5\textsf{.} Combine x2x^2 terms: 9x2−3x2=6x2.9x^2 - 3x^2 = 6x^2\textsf{.} The xx terms cancel: −4x+4x=0.-4x + 4x = 0\textsf{.} The constant is −5.-5\textsf{.} Result: 6x2−5.6x^2 - 5\textsf{.}

Buzzer beatermedium

Simplify: (7x2+2x−3)−(5x2−2x+1).(7x^2 + 2x - 3) - (5x^2 - 2x + 1)\textsf{.}

Distribute the minus sign: (7x2+2x−3)−5x2+2x−1.(7x^2 + 2x - 3) - 5x^2 + 2x - 1\textsf{.} Combine x2x^2 terms: 7x2−5x2=2x2.7x^2 - 5x^2 = 2x^2\textsf{.} Combine xx terms: 2x+2x=4x.2x + 2x = 4x\textsf{.} Combine constants: −3−1=−4.-3 - 1 = -4\textsf{.} Result: 2x2+4x−4.2x^2 + 4x - 4\textsf{.}

Overtime

2 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
Tests that cover polynomial combining like terms (act/sat):
SBACACTPARCCNY State MathNC EOG/EOC
Reporting domains for this skill
ACT All grades: Preparing for Higher MathSTAAR Algebra I: Number and Algebraic MethodsSBAC High School: Concepts and ProceduresACT Aspire All grades: Preparing for Higher MathAK STAR Grade 9: AlgebraATLAS Algebra I: Algebra
More Grade 9 skills
Piecewise function composition (ACT)Polynomial expression multiplication (SAT)Monomial expression multiplication (SAT)Product systems that compare numbersLiteral quadratic equations (ACT)Quadratic distinct real solutions countLiteral equations (SAT)Quadratic expression values from equationsAll Grade 9 practice →

Drill it inside a game.

The free placement test finds your level, then every match serves polynomial combining like terms (act/sat) questions at exactly the right difficulty.