More complex binomial products | Maths | Quizalize & Oak National Academy

Starter quiz

Which of these expressions are binomials?
- $x - 8$ ✓
- $2a + 4$ ✓
- $x^2 + 4x + 4$
- $3y - 2x$ ✓
- $2xy$
Which of these are equivalent to $a - 6$ ?
- $6 - a$
- $-a + 6$
- $-6 + a$ ✓
- $-6a$
In the expression $6x + 4$ , you call 6 the ______ of $x$ .
- 'coefficient' ✓
Match each product to its simplified form.
- $x \times -x$
  
  ⇔
  
  $-x^2$ ✓
- $-x\times -x$
  
  ⇔
  
  $x^2$ ✓
- $-2x \times -3x$
  
  ⇔
  
  $6x^2$ ✓
- $-6x \times y$
  
  ⇔
  
  $-6xy$ ✓
- $-3y \times -2x$
  
  ⇔
  
  $6xy$ ✓
- $6x\times -x$
  
  ⇔
  
  $-6x^2$ ✓
Which of these expressions can be written as the difference of two squares?
- $(x-29)^2$
- $(x + 29)(x - 20)$
- $(x + 29)(x - 29)$ ✓
- $(x - 9)(x - 9)$
- $(x - 9)(y + 9)$
Match each product of two binomials to its expanded form.
- $(x - 5)^2$
  
  ⇔
  
  $x^2 - 10x + 25$ ✓
- $(x - 4)(x - 6)$
  
  ⇔
  
  $x^2 - 10x + 24$ ✓
- $(x + 2)(x - 12)$
  
  ⇔
  
  $x^2 - 10x - 24$ ✓
- $(x + 4)(x - 6)$
  
  ⇔
  
  $x^2 - 2x - 24$ ✓
- $(x + 4)(x + 6)$
  
  ⇔
  
  $x^2 + 10x + 24$ ✓
- $(x + 12)(x - 2)$
  
  ⇔
  
  $x^2 + 10x - 24$ ✓

Exit quiz

Which binomial expression is equivalent to $8 - x$ ?
- $x - 8$
- $x - (-8)$
- $-x + 8$ ✓
- $-x - 8$
Which product of two binomials is equivalent to $(x - 5)(5 - x)$ ?
- $(x - 5)^2$
- $(5 - x)^2$
- $(x - 5)(-x -5)$
- $(x - 5)(-x + 5)$ ✓
- $(5 - x)( -5 + x)$ ✓
Which of these expressions can be written as the difference of two squares?
- $(a - b)(b - a)$
- $(1 - a)(a + 1)$ ✓
- $(a - b)(-b - a)$ ✓
- $(6 - b)(-b + 6)$
- $(a - 4)(4 + b)$
Match each product of two binomials to its expanded form.
- $(x + 4)(4 -x)$
  
  ⇔
  
  $-x^2 +16$ ✓
- $(x - 4)(4 -x)$
  
  ⇔
  
  $-x^2 +8x -16$ ✓
- $(x - 4)(4 + x)$
  
  ⇔
  
  $x^2 -16$ ✓
- $(x - 4)(-4 +x)$
  
  ⇔
  
  $x^2 - 8x + 16$ ✓
$(3x -1)(2x + 5)$ can be expanded and simplified to give $6x^2 +$ ______ $x - 5$ .
- '13' ✓
Expand and simplify $(2b - 3a)(2a - 3b)$ .
- $-6a^2 -5ab-6b^2$
- $5ab-6a^2-6b^2$
- $6a^2 +6b^2-13ab$
- $6b^2-6a^2-5ab$
- $13ab-6b^2-6a^2$ ✓

Worksheet

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Lesson Details

Key learning points

The coefficients of the variable(s) may not be one.
Sometimes the terms within each binomial are not in the same order.
Multiplication and addition/subtraction with negative numbers is useful here.

Common misconception

Mistakes with partial products are even more common where algebraic terms in the binomials have coefficients greater than 1. It is common to find pupils writing that the product of 2x and 3x is 5x

Reminding pupils that because multiplication is commutative the product of 2x and 3x can be thought of as 2 × 3 × x × x

Keywords

Binomial - A binomial is an algebraic expression representing the sum of exactly 2 unlike terms.