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.

Q1:

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

Q2:

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©

Q3:

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

Q4:

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©

Q5:

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©

Q6:

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

Q7:

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©

Q8:

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

Q9:

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

Q10:

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

Practice Means Progress

Download the Nagwa Practice app to access 29 additional questions for this lesson!

scan me!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.