Lesson Worksheet: Multiplying a Binomial by an Algebraic Expression Mathematics • 9th Grade

In this worksheet, we will practice multiplying a binomial by a polynomial of order three and similar algebraic expressions.


Simplify the expression (π‘₯+2)ο€Ήπ‘₯βˆ’5π‘₯+3ο…οŠ¨.

  • Aπ‘₯+7π‘₯+13π‘₯+6
  • Bπ‘₯+5π‘₯+11π‘₯+10
  • Cπ‘₯βˆ’3π‘₯βˆ’7π‘₯+6
  • Dπ‘₯βˆ’π‘₯βˆ’π‘₯+10
  • Eπ‘₯+7π‘₯+7π‘₯βˆ’6


Expand the expression (π‘₯+2𝑦)ο€Ήπ‘₯βˆ’4π‘₯𝑦+3π‘¦ο…οŠ¨οŠ¨, giving your answer in its simplest form.

  • Aπ‘₯βˆ’π‘₯π‘¦βˆ’10π‘₯𝑦+6π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • Bπ‘₯βˆ’2π‘₯π‘¦βˆ’5π‘₯𝑦+6π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • Cπ‘₯+6π‘₯𝑦+5π‘₯π‘¦βˆ’6π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • Dπ‘₯+2π‘₯π‘¦βˆ’5π‘₯π‘¦βˆ’6π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • Eπ‘₯+6π‘₯𝑦+11π‘₯𝑦+6π‘¦οŠ©οŠ¨οŠ¨οŠ©


What does the expression (π‘₯+2)(π‘₯βˆ’7)(π‘₯+4) simplify to?

  • Aπ‘₯βˆ’5π‘₯βˆ’22π‘₯+56
  • Bπ‘₯βˆ’π‘₯βˆ’34π‘₯βˆ’56
  • Cπ‘₯+5π‘₯βˆ’22π‘₯βˆ’56
  • Dπ‘₯+9π‘₯+6π‘₯βˆ’56
  • Eπ‘₯+13π‘₯+50π‘₯+56


What does the expression (π‘₯βˆ’2𝑦)(π‘₯+4𝑦)(π‘₯+𝑦) simplify to?

  • Aπ‘₯βˆ’5π‘₯𝑦+2π‘₯𝑦+8π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • Bπ‘₯+5π‘₯𝑦+2π‘₯π‘¦βˆ’8π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • Cπ‘₯βˆ’π‘₯π‘¦βˆ’10π‘₯π‘¦βˆ’8π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • Dπ‘₯+7π‘₯𝑦+14π‘₯𝑦+8π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • Eπ‘₯+3π‘₯π‘¦βˆ’6π‘₯π‘¦βˆ’8π‘¦οŠ©οŠ¨οŠ¨οŠ©


Expand the expression (5π‘₯+2𝑦)(π‘¦βˆ’2π‘₯), giving your answer in its simplest form.

  • A20π‘₯βˆ’12π‘₯π‘¦βˆ’3π‘₯𝑦+2π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • B20π‘₯+12π‘₯π‘¦βˆ’3π‘₯π‘¦βˆ’2π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • C5π‘₯βˆ’18π‘₯𝑦+12π‘₯𝑦+8π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • D5π‘₯βˆ’22π‘₯𝑦+28π‘₯π‘¦βˆ’8π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • E20π‘₯βˆ’28π‘₯𝑦+13π‘₯π‘¦βˆ’2π‘¦οŠ©οŠ¨οŠ¨οŠ©


Simplify the algebraic expression (π‘₯βˆ’2)(π‘₯+6).

  • Aπ‘₯+2π‘₯βˆ’20π‘₯+24
  • Bπ‘₯βˆ’10π‘₯+12π‘₯+72
  • Cπ‘₯+14π‘₯+60π‘₯+72
  • Dπ‘₯+10π‘₯+12π‘₯βˆ’72
  • Eπ‘₯βˆ’14π‘₯+60π‘₯βˆ’72


Using the multiplication of a binomial by a trinomial, simplify the algebraic expression (3π‘₯+2𝑦).

  • A27π‘₯+54π‘₯𝑦+36π‘₯𝑦+8π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • B27π‘₯+135π‘₯𝑦+225π‘₯𝑦+125π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • C8π‘₯+36π‘₯𝑦+54π‘₯𝑦+27π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • D27π‘₯+108π‘₯𝑦+144π‘₯𝑦+64π‘¦οŠ©οŠ¨οŠ¨οŠ©
  • E8π‘₯+48π‘₯𝑦+96π‘₯𝑦+64π‘¦οŠ©οŠ¨οŠ¨οŠ©


If (π‘₯+π‘˜)ο€Ήπ‘₯βˆ’4π‘₯+9=π‘₯βˆ’11π‘₯+37π‘₯βˆ’63, find the value of parameter π‘˜.


A rectangular prism has its base area given by the trinomial ο€Ή2π‘₯+7π‘₯𝑦+2π‘¦ο…οŠ¨οŠ¨ cm2 and its height given by the binomial (π‘₯+𝑦) cm. Find its volume.

  • A2π‘₯+11π‘₯𝑦+15π‘₯𝑦+2π‘¦οŠ©οŠ¨οŠ¨οŠ© cm3
  • B2π‘₯+8π‘₯𝑦+8π‘₯𝑦+2π‘¦οŠ©οŠ¨οŠ¨οŠ© cm3
  • C2π‘₯+15π‘₯𝑦+11π‘₯𝑦+2π‘¦οŠ©οŠ¨οŠ¨οŠ© cm3
  • D2π‘₯+9π‘₯𝑦+9π‘₯𝑦+2π‘¦οŠ©οŠ¨οŠ¨οŠ© cm3
  • E2π‘₯+16π‘₯𝑦+16π‘₯𝑦+2π‘¦οŠ©οŠ¨οŠ¨οŠ© cm3


A rectangular prism has a square base of length (3π‘₯+2𝑦) m and a height of length (2𝑦+π‘₯) m. Find its volume in terms of π‘₯ and 𝑦.

  • A9π‘₯+30π‘₯𝑦+28π‘₯𝑦+8π‘¦οŠ©οŠ¨οŠ¨οŠ© m3
  • B18π‘₯+33π‘₯𝑦+20π‘₯𝑦+4π‘¦οŠ©οŠ¨οŠ¨οŠ© m3
  • C4π‘₯+20π‘₯𝑦+33π‘₯𝑦+18π‘¦οŠ©οŠ¨οŠ¨οŠ© m3
  • D3π‘₯+14π‘₯𝑦+20π‘₯𝑦+8π‘¦οŠ©οŠ¨οŠ¨οŠ© m3
  • E8π‘₯+28π‘₯𝑦+30π‘₯𝑦+9π‘¦οŠ©οŠ¨οŠ¨οŠ© m3

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