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 (𝑥+2)𝑥5𝑥+3.

  • A𝑥+7𝑥+13𝑥+6
  • B𝑥+5𝑥+11𝑥+10
  • C𝑥3𝑥7𝑥+6
  • D𝑥𝑥𝑥+10
  • E𝑥+7𝑥+7𝑥6

Q2:

Expand the expression (𝑥+2𝑦)𝑥4𝑥𝑦+3𝑦, giving your answer in its simplest form.

  • A𝑥𝑥𝑦10𝑥𝑦+6𝑦
  • B𝑥2𝑥𝑦5𝑥𝑦+6𝑦
  • C𝑥+6𝑥𝑦+5𝑥𝑦6𝑦
  • D𝑥+2𝑥𝑦5𝑥𝑦6𝑦
  • E𝑥+6𝑥𝑦+11𝑥𝑦+6𝑦

Q3:

What does the expression (𝑥+2)(𝑥7)(𝑥+4) simplify to?

  • A𝑥5𝑥22𝑥+56
  • B𝑥𝑥34𝑥56
  • C𝑥+5𝑥22𝑥56
  • D𝑥+9𝑥+6𝑥56
  • E𝑥+13𝑥+50𝑥+56

Q4:

What does the expression (𝑥2𝑦)(𝑥+4𝑦)(𝑥+𝑦) simplify to?

  • A𝑥5𝑥𝑦+2𝑥𝑦+8𝑦
  • B𝑥+5𝑥𝑦+2𝑥𝑦8𝑦
  • C𝑥𝑥𝑦10𝑥𝑦8𝑦
  • D𝑥+7𝑥𝑦+14𝑥𝑦+8𝑦
  • E𝑥+3𝑥𝑦6𝑥𝑦8𝑦

Q5:

Expand the expression (5𝑥+2𝑦)(𝑦2𝑥), giving your answer in its simplest form.

  • A20𝑥12𝑥𝑦3𝑥𝑦+2𝑦
  • B20𝑥+12𝑥𝑦3𝑥𝑦2𝑦
  • C5𝑥18𝑥𝑦+12𝑥𝑦+8𝑦
  • D5𝑥22𝑥𝑦+28𝑥𝑦8𝑦
  • E20𝑥28𝑥𝑦+13𝑥𝑦2𝑦

Q6:

Simplify the algebraic expression (𝑥2)(𝑥+6).

  • A𝑥+2𝑥20𝑥+24
  • B𝑥10𝑥+12𝑥+72
  • C𝑥+14𝑥+60𝑥+72
  • D𝑥+10𝑥+12𝑥72
  • E𝑥14𝑥+60𝑥72

Q7:

Using the multiplication of a binomial by a trinomial, simplify the algebraic expression (3𝑥+2𝑦).

  • A27𝑥+54𝑥𝑦+36𝑥𝑦+8𝑦
  • B27𝑥+135𝑥𝑦+225𝑥𝑦+125𝑦
  • C8𝑥+36𝑥𝑦+54𝑥𝑦+27𝑦
  • D27𝑥+108𝑥𝑦+144𝑥𝑦+64𝑦
  • E8𝑥+48𝑥𝑦+96𝑥𝑦+64𝑦

Q8:

If (𝑥+𝑘)𝑥4𝑥+9=𝑥11𝑥+37𝑥63, find the value of parameter 𝑘.

Q9:

A rectangular prism has its base area given by the trinomial 2𝑥+7𝑥𝑦+2𝑦 cm2 and its height given by the binomial (𝑥+𝑦) cm. Find its volume.

  • A2𝑥+11𝑥𝑦+15𝑥𝑦+2𝑦 cm3
  • B2𝑥+8𝑥𝑦+8𝑥𝑦+2𝑦 cm3
  • C2𝑥+15𝑥𝑦+11𝑥𝑦+2𝑦 cm3
  • D2𝑥+9𝑥𝑦+9𝑥𝑦+2𝑦 cm3
  • E2𝑥+16𝑥𝑦+16𝑥𝑦+2𝑦 cm3

Q10:

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

  • A9𝑥+30𝑥𝑦+28𝑥𝑦+8𝑦 m3
  • B18𝑥+33𝑥𝑦+20𝑥𝑦+4𝑦 m3
  • C4𝑥+20𝑥𝑦+33𝑥𝑦+18𝑦 m3
  • D3𝑥+14𝑥𝑦+20𝑥𝑦+8𝑦 m3
  • E8𝑥+28𝑥𝑦+30𝑥𝑦+9𝑦 m3

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