Worksheet: Squaring Binomials

In this worksheet, we will practice expanding the square of the difference or sum of two monomials.

Q1:

Expand ( 𝑚 + 4 ) 2 .

  • A 𝑚 + 8 𝑚 + 8 2
  • B 𝑚 + 4 𝑚 + 1 6 2
  • C 𝑚 + 4 𝑚 + 8 2
  • D 𝑚 + 8 𝑚 + 1 6 2
  • E 2 𝑚 + 8 𝑚 + 1 6 2

Q2:

Expand ( 2 𝑥 + 5 ) 2 .

  • A 4 𝑥 + 1 0 𝑥 + 2 5 2
  • B 4 𝑥 2 0 𝑥 + 2 5 2
  • C 4 𝑥 + 2 0 𝑥 + 1 0 2
  • D 4 𝑥 + 2 0 𝑥 + 2 5 2
  • E 4 𝑥 + 1 0 𝑥 + 1 0 2

Q3:

Expand ( 3 𝑥 + 4 ) 2 .

  • A 9 𝑥 + 2 4 𝑥 1 6 2
  • B 9 𝑥 2 4 𝑥 + 1 6 2
  • C 9 𝑥 2 4 𝑥 1 6 2
  • D 9 𝑥 + 2 4 𝑥 + 1 6 2
  • E 9 𝑥 + 1 6 2

Q4:

Expand ( 𝑚 4 ) 2 .

  • A 𝑚 8 𝑚 + 8 2
  • B 𝑚 + 8 𝑚 + 1 6 2
  • C 𝑚 4 𝑚 + 1 6 2
  • D 𝑚 8 𝑚 + 1 6 2
  • E 𝑚 + 4 𝑚 + 1 6 2

Q5:

Expand ( 𝑥 + 2 𝑦 ) 2 .

  • A 𝑥 2 𝑥 𝑦 + 4 𝑦 2 2
  • B 𝑥 + 4 𝑦 2 2
  • C 𝑥 4 𝑥 𝑦 4 𝑦 2 2
  • D 𝑥 4 𝑥 𝑦 + 4 𝑦 2 2
  • E 𝑥 + 4 𝑥 𝑦 + 4 𝑦 2 2

Q6:

Expand 4 𝑥 + 3 2 𝑦 2 2 2 .

  • A 1 6 𝑥 + 6 𝑥 𝑦 + 9 4 𝑦 4 2 2 4
  • B 1 6 𝑥 + 9 4 𝑦 4 4
  • C 1 6 𝑥 1 2 𝑥 𝑦 + 9 4 𝑦 4 2 2 4
  • D 1 6 𝑥 + 1 2 𝑥 𝑦 + 9 4 𝑦 4 2 2 4

Q7:

Expand the brackets and simplify ( 8 𝑥 2 𝑦 ) ( 8 𝑥 + 2 𝑦 ) 2 2 .

  • A 3 2 𝑥 𝑦
  • B 1 2 8 𝑥 + 8 𝑦 2 2
  • C 6 4 𝑥 8 𝑦 2 2
  • D 6 4 𝑥 𝑦

Q8:

Expand and simplify ( 𝑥 + 2 ) ( 𝑥 + 2 ) .

  • A 𝑥 + 4 2
  • B 𝑥 + 4 2
  • C 𝑥 + 4 𝑥 4 2
  • D 𝑥 + 4 𝑥 + 4 2
  • E 𝑥 4 𝑥 + 4 2

Q9:

Expand ( 𝑚 4 ) 2 .

  • A 𝑚 8 𝑚 + 8 2
  • B 𝑚 + 8 𝑚 + 1 6 2
  • C 𝑚 4 𝑚 + 1 6 2
  • D 𝑚 8 𝑚 + 1 6 2
  • E 𝑚 + 4 𝑚 + 1 6 2

Q10:

Expand ( 2 𝑥 + 5 ) 2 .

  • A 4 𝑥 + 1 0 𝑥 + 2 5 2
  • B 4 𝑥 2 0 𝑥 + 2 5 2
  • C 4 𝑥 + 2 0 𝑥 + 1 0 2
  • D 4 𝑥 + 2 0 𝑥 + 2 5 2
  • E 4 𝑥 + 1 0 𝑥 + 1 0 2

Q11:

Expand ( 𝑚 + 4 ) 2 .

  • A 𝑚 + 8 𝑚 + 8 2
  • B 𝑚 + 4 𝑚 + 1 6 2
  • C 𝑚 + 4 𝑚 + 8 2
  • D 𝑚 + 8 𝑚 + 1 6 2
  • E 2 𝑚 + 8 𝑚 + 1 6 2

Q12:

If ( 𝑥 + 𝑦 ) = 1 0 0 2 and 𝑥 𝑦 = 2 0 , what is the value of 𝑥 + 𝑦 2 2 ?

Q13:

Given that 𝑥 + 𝑦 = 7 7 2 2 and 𝑥 𝑦 = 1 4 , what are the possible values of 𝑥 𝑦 ?

  • A 3 1 , 3 1
  • B 7
  • C 9 , 9
  • D 7 , 7
  • E 9

Q14:

If 𝑥 + 𝑦 = 9 3 2 2 and 𝑥 𝑦 = 6 , what is the value of ( 𝑥 𝑦 ) 2 ?

Q15:

If 𝑥 + 9 𝑦 = 1 5 2 2 and 𝑥 𝑦 = 2 , what is the value of ( 𝑥 3 𝑦 ) 2 ?

Q16:

Expand ( 𝑥 4 𝑦 ) 2 .

  • A 𝑥 + 4 𝑥 𝑦 + 1 6 𝑦 2 2
  • B 𝑥 + 1 6 𝑦 2 2
  • C 𝑥 + 8 𝑥 𝑦 1 6 𝑦 2 2
  • D 𝑥 + 8 𝑥 𝑦 + 1 6 𝑦 2 2
  • E 𝑥 8 𝑥 𝑦 + 1 6 𝑦 2 2

Q17:

Expand ( 4 𝑥 + 6 𝑦 ) 2 .

  • A 1 6 𝑥 + 2 4 𝑥 𝑦 + 3 6 𝑦 2 2
  • B 1 6 𝑥 + 3 6 𝑦 2 2
  • C 1 6 𝑥 + 4 8 𝑥 𝑦 3 6 𝑦 2 2
  • D 1 6 𝑥 + 4 8 𝑥 𝑦 + 3 6 𝑦 2 2
  • E 1 6 𝑥 4 8 𝑥 𝑦 + 3 6 𝑦 2 2

Q18:

Expand ( 5 𝑥 + 4 𝑦 ) 2 .

  • A 2 5 𝑥 2 0 𝑥 𝑦 + 1 6 𝑦 2 2
  • B 2 5 𝑥 + 1 6 𝑦 2 2
  • C 2 5 𝑥 4 0 𝑥 𝑦 1 6 𝑦 2 2
  • D 2 5 𝑥 4 0 𝑥 𝑦 + 1 6 𝑦 2 2
  • E 2 5 𝑥 + 4 0 𝑥 𝑦 + 1 6 𝑦 2 2

Q19:

Expand 2 𝑥 + 3 2 𝑦 2 .

  • A 4 𝑥 3 𝑥 𝑦 + 9 4 𝑦 2 2
  • B 4 𝑥 + 9 4 𝑦 2 2
  • C 4 𝑥 + 6 𝑥 𝑦 + 9 4 𝑦 2 2
  • D 4 𝑥 6 𝑥 𝑦 + 9 4 𝑦 2 2

Q20:

Expand 9 𝑥 1 2 𝑦 2 .

  • A 8 1 𝑥 9 2 𝑥 𝑦 + 1 4 𝑦 2 2
  • B 8 1 𝑥 + 1 4 𝑦 2 2
  • C 8 1 𝑥 + 9 𝑥 𝑦 + 1 4 𝑦 2 2
  • D 8 1 𝑥 9 𝑥 𝑦 + 1 4 𝑦 2 2
  • E 8 1 𝑥 9 𝑥 𝑦 1 4 𝑦 2 2

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