Year 9 Interactive Maths - Second Edition

Cross-Multiplication Method

Place the linear factors one above the other as shown below.

Multiply the numbers along the arms of the cross, and then add the products.  That is,
 x×10 + x×1 = 10x+ x = 11x.  This is not the middle term.

 x×5 + x×2 = 5x+ 2x = 7x.  This is the middle term.

Note:

• The solution is read across.
• 10 = 1 × 10 = 2 × 5 = –1 × –10 = –2 × –5
  We did not try –1 × –10 and –2 × –5 because the middle term is positive.
• The answer can be checked using the Distributive Law.  That is:
  
  

Example 13

Factorise the following:

Solution:

     Multiply the numbers along the arms of the cross, and then add the products.
      x×15 + x×1 = 15x+ x = 16x.  This is not the middle term.

     We reject this pair as the middle term is 8x.  Now, try the next pair.

      x×5 + x×3 = 5x+ 3x = 8x.  We accept this pair as the middle term is 8x.

      x× – 4 + x× –3 = – 4x – 3x = –7x.  We accept this pair as the middle term is –7x.

Note:

We did not try 1 × 12, 2 × 6 and 3 × 4 because the middle term is negative.  Also, we did not try
–2 × –6 and –1 × –12 because we have already obtained the middle term by using –3 × – 4.

      x × 7 + x × –1 = 7x – x = 6x.  We accept this pair as the middle term is 6x.

Note:

We did not try 1 × –7 because we have already obtained the middle term by using –1 × 7.

Note:

We did not try –1 × 8, –2 × 4 and 2 × – 4 because we have already obtained the middle term by using 1 × –8.

Key Terms

cross-multiplication method