Expanding Binomials Expand the product of binomials expansion
Expanding Binomials Expand the product of binomials. (expansion of 2 – grade 5, expansion of more than 2 – grade 6) If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk
Key Vocabulary Expand – multiply out Binomial Quadratic Cubic Linear Collect Constant Negative Product
x×x= x 2 2 x × 2 x = 2 x 2 y÷y=y g 3 × g 5 = 5 a × 3 b = 15 ab g 8 There are sixteen statements on the slide. 5 p − 4 p = p y × y = 2 y x × x 2 = x 3 Half are true (these turn green when you click them). Half are false (these turn red). − 3 n × − 2 n 6 a + the 2 b true statements. 3 f − 5 f Find 6 q ÷ 2 q = 3 2 is wrong with each of the others. = − 2 f = − 6 n Explain what = 8 ab 3 a × b = 4 ab m 2 × m 4 = m 8 −m × − 2 m = 2 m 2 Skip this activity z + z = z 2
Expanding brackets single 34 cm 3 × 34 3 cm 30 cm 4 cm 3 × 30 3× 4 Click on a box to learn more about it. Click anywhere else to advance the slide
Expanding brackets single x+5 2 2 22(x × (x++5)5) x 5 22 x ×x 210 × 5 Click on a blank box to learn more about it. Click on any blue text to simplify it. Click anywhere else to advance the slide
Expanding brackets practice (1) BRONZE 1. 2. 3. 4. 5. 6. 3(x+4) 5(y+2) 2(x− 6) x(x+8) y(y+3) n(n− 5) SILVER 7. 8. 9. 10. 11. 12. 5 ( 2 x + 1 ) 3 ( 4 y + z ) 2 ( p − 4 q ) x(x+y) p ( 4 p + 3 q ) m ( 2 m − 3 n ) SILVER 19. 20. 21. 22. 23. 24. 5(x+1)+2(x+3) 5(y+3)+7(y+1) 3(x− 6)+5(x− 6) 5(x+2)+2(x− 7) 4(y+6)− 3(y− 1) 3(n− 4)− 5(n− 7) GOLD 13. 14. 15. 16. 17. 18. 4 x ( x + y ) 2 y ( y + z ) 2 x ( x − 3 w ) 3 x ( 2 x + z ) 4 y ( 2 y + 3 z ) 5 m ( 2 m − 7 n ) GOLD 25. 26. 27. 28. 29. 30. 6 ( 2 x + 3 ) − 2 ( 3 x + 3 ) 8 ( y + 4 ) − 3 ( 2 y + 1 ) x ( 5 x − 6 ) + x ( x + 4 ) x ( x + 8 ) + x ( 3 x + 7 ) y(y+1)+y(y− 2) m(m− 6)+m(m− 7)
Expanding brackets two single 3( x + 5 ) + 2( x + 4 ) 3 x + 15 2 x + 8 5 x + 23
Expanding brackets practice (1) BRONZE 1. 2. 3. 4. 5. 6. 3(x+4) 5(y+2) 2(x− 6) x(x+8) y(y+3) n(n− 5) SILVER 7. 8. 9. 10. 11. 12. 5 ( 2 x + 1 ) 3 ( 4 y + 3 ) 2 ( 3 x − 4 ) x ( 3 x + 1 ) p ( 4 p + 3 ) m ( 2 m − 3 ) SILVER 19. 20. 21. 22. 23. 24. 5(x+1)+2(x+3) 5(y+3)+7(y+1) 3(x− 6)+5(x− 6) 5(x+2)+2(x− 7) 4(y+6)− 3(y− 1) 3(n− 4)− 5(n− 7) GOLD 13. 14. 15. 16. 17. 18. 4 x ( x + y ) 2 y ( y + z ) 2 x ( x − 3 w ) 3 x ( 2 x + z ) 4 y ( 2 y + 3 z ) 5 m ( 2 m − 7 n ) GOLD 25. 26. 27. 28. 29. 30. 6(x+3)− 2(x+3) 8(y+4)− 3(y+1) x(x− 6)+x(x+4) x(x+8)+x(x+7) y(y+1)+y(y− 2) m(m− 6)+m(m− 7)
3( x + 5 ) + 2( x + 4 ) (x + 5)×(x + 8) Tell me three ways in which these two expressions differ
Expanding numerical demo 49 27 20800 × 40 20180 × 9 20 7280 × 40 763 × 9 7 40 9 800 + 180 + 280 + 63 1323 Click on a blank box to learn more about it. Click on any blue text to simplify it. Click anywhere else to advance the slide
Expanding double brackets demo x+8 x+5 x x× 2 x 88 x ×x x x 5 x × 5 840 × 5 5 x 8 x 2 + 5 x + 8 x + 40 x 2 + 13 x + 40 Click on a blank box to learn more about it. Click on any blue text to simplify it. Click anywhere else to advance the slide
FOIL method (demo 1)
FOIL method (demo 2)
FOIL method (demo 3)
FOIL method (demo 4)
FOIL method (demo 5) •
Expanding brackets practice (2) BRONZE 1. 2. 3. 4. 5. 6. SILVER ( x + 4 )( x + 2 ) ( x + 6 )( x + 9 ) ( x + 7 )( x + 3 ) ( x + 1 )( x + 6 )( x + 1 ) ( x + 8 )( x + 5 ) 7. 8. 9. 10. 11. 12. ( x − 3 )( x + 7 ) ( x + 6 )( x − 5 ) ( x + 2 )( x − 4 ) ( x − 6 )( x + 2 ) ( x − 3 )( x − 4 ) ( x − 6 )( x − 2 ) SILVER Take extra care here with negative signs. What does ( g + 6 )2 mean? Think about how to start this question. Have you made sure you have fully simplified all your answers? 13. 14. 15. 16. 17. 18. GOLD ( y − 1 )( y + 4 ) ( p + 2 )( p − 6 ) ( n + 1 )( n − 7 ) ( g + 6 )2 ( z − 3 )2 ( a − 9)2 19. 20. 21. 22. 23. 24. ( 2 y + 3 )( y + 1 ) ( n + 6 )( 3 n − 5 ) ( 3 a − b )( 2 a − b ) ( x − 6 )( x + 6 ) ( m + 3 )( m − 3 ) ( a − b )( a + b ) GOLD Finished? Now look at your answers to questions 22, 23 and 24. They all have something in common – in fact they are linked by a rule. Can you see what it is?
Expanding brackets practice (3) Can you make the expressions in blue from the factors in yellow? (Actually, no you can’t – there are 8 expressions but only 12 factors, where you would need to have 16 altogether. ) When you have sorted them, there will be two expressions left over that can’t be made from any brackets. Can you work out why not? x 2 + 6 x + 8 x 2 + x − 20 x 2 + 3 x − 18 (x+3) (x− 6) (x+2) (x− 4) (x− 3) (x+4) x 2 − 2 x − 8 (x+5) (x+2) (x− 4) x 2 + 4 x 2 − 16 (x+6) (x+4) (x− 4) x 2 − 3 x − 18 x 2 + 2 x + 5
Expanding brackets practice (4) If this is the answer, what is the question? All but two of the expressions below, can be made by multiplying together a pair of brackets. Can you find a pair of brackets for those that can be done – and how about explaining why the other two don’t work? x 2 + 8 x + 15 x 2 + 6 x + 12 x 2 + 7 x − 18 x 2 + x − 30 x 2 + 6 x + 9 x 2 + x x 2 + 9 x 2 − 25 x 2 − 2 x (What you are actually doing is called factorising. This is the opposite of expanding – instead of taking the brackets out, you are putting them in). Click on a box to see if it will factorise. If it turns red, it won’t. If it turns green, you know what to do…
Expanding more than 2 binomials (higher only) 1. Expand two brackets (x – 5) (x + 2) 2. Expand answer with (x + 7) 3. Simplify by collecting like terms
Expanding more than 2 binomials practice (higher only)
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