T Madas What is 47 x 12 47

This property of numbers is very useful in algebra: 2 x ( a +

This property of numbers is very useful in algebra: 2 ( p – q

The operation of removing brackets is called: “expanding the brackets” or “multiplying out the

We can use areas to show why the operation of “expanding brackets” works: 3

We can use areas to show why the operation of “expanding brackets” works: a–

Algebra with Expanding Brackets © T Madas

algebra involving bracket expansions 2 (x + 4 ) + 3 (x – 2

“expand” the following brackets: 3(a + b ) = 3 a + 3 b

“expand” the following brackets: 2(x + y ) = 2 x + 2 y

“expand” the following brackets: 4(x + y ) = 4 x + 4 y

“expand” the following brackets: 3(2 a + b ) = 6 a + 3

“expand” the following brackets: 3(3 b – 4 c ) = 9 b –

Quick Test on Expanding Brackets © T Madas

Which two of the following expressions are equivalent? 5(3 x + 10) 15 x

Which of the following expressions are NOT correct factorisations of 24 x + 12?

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What is 47 x 12? 47 x 10 = 470 47 x 2 = 94 564 470 or 47 x 12 = 47 x (10 + 2) 94 © T Madas

17 x 12 17 x (10 + 2) = 17 x 10 + 17 x 2 = 204 = 170 + 34 25 x 23 25 x (20 + 3) = 25 x 20 + 25 x 3 = 575 = 500 + 75 34 x 9 34 x (10 – 1) = 34 x 10 – 34 x 1 = 306 = 340 – 34 © T Madas

This property of numbers is very useful in algebra: 2 x ( a + b ) = 2 x a + 2 x b = 2 a + 2 b 3 x ( n + 2 ) = 3 x n + 3 x 2 = 3 n + 6 4 x ( a – 3 ) = 4 x a – 4 x 3 = 4 a – 12 © T Madas

This property of numbers is very useful in algebra: 2 ( p – q ) = 2 x p – 2 x q = 2 p – 2 q 6 ( y – 2 ) = 6 x y – 6 x 2 = 6 y – 12 4 (2 a + 5 ) = 4 x 2 a + 4 x 5 = 8 a + 20 © T Madas

The operation of removing brackets is called: “expanding the brackets” or “multiplying out the brackets” © T Madas

We can use areas to show why the operation of “expanding brackets” works: 3 x 2 3 x 6 x+2 3 ( x + 2 ) = 3 x + 6 © T Madas

We can use areas to show why the operation of “expanding brackets” works: a– 2 2 4 a 4 4(a – 2) 8 a 4 ( a – 2 ) = 4 a – 8 © T Madas

Algebra with Expanding Brackets © T Madas

algebra involving bracket expansions 2 (x + 4 ) + 3 (x – 2 ) = 2 x + 8 + 3 x – 6 = 5 x + 2 2 ( x + y ) + 3 (2 x – y ) = 2 x + 2 y + 6 x – 3 y = 8 x – y 3 (a + 2 ) + 5 (a – 3 ) = 3 a + 6 + 5 a – 15 = 8 a – 9 5 ( p + 3 ) + 2 (2 – p ) = 5 p + 15 + 4 – 2 p = 3 p + 19 4 ( t + 2 ) + 3 ( 2 t + 3 ) = 3 (4 + n ) + 4 (2 n – 5 ) = 12 + 3 n + 8 n – 20 = 4 t + 8 + 6 t + 9 = 11 n – 8 10 t + 17 © T Madas

Practice Expanding Brackets © T Madas

“expand” the following brackets: 3(a + b ) = 3 a + 3 b 4(p – q ) = 4 p – 4 q 2(x + 4 ) = 2 x + 8 7(x + 3 ) = 7 x + 21 2(w + 1 ) = 2 w + 2 3(v + 5 ) = 3 v + 15 3(x – y ) = 3 x – 3 y 3(3 + n ) = 9 + 3 n 4(p + 3 ) = 4 p + 12 2(4 – x ) = 8 – 2 x 2(f – 5 ) = 2 f – 10 2(8 – c ) = 16 – 2 c 2(4 + a ) = 8 + 2 a 6(c – 3 ) = 6 c – 18 5(1 + t ) = 5 + 5 t 6(y – 4 ) = 6 y – 24 © T Madas

“expand” the following brackets: 2(x + y ) = 2 x + 2 y 3(p – q ) = 3 p – 3 q 4(d + 2 ) = 4 d + 8 8(y + 3 ) = 8 y + 24 3(k + 1 ) = 3 k + 3 4(u + 5 ) = 4 u + 20 5(x – y ) = 5 x – 5 y 3(2 + n ) = 6 + 3 n 2(p + 7 ) = 2 p + 14 4(2 – x ) = 8 – 4 x 3(g – 5 ) = 3 g – 15 6(5 – a ) = 30 – 6 a 2(4 + r ) = 8 + 2 r 3(4 + t ) = 12 + 3 t 6(s – 5 ) = 6 s – 30 5(z – 4 ) = 5 z – 20 5(a + b – 3) = 5 a + 5 b – 15 © T Madas

“expand” the following brackets: 4(x + y ) = 4 x + 4 y 3(6 – q ) = 18 – 3 q 2(d + 3 ) = 2 d + 6 8(y + 2 ) = 8 y + 16 3(k – 1 ) = 3 k – 3 7(u + 6 ) = 7 u + 42 7(a – b ) = 7 a – 7 b 3(3 + n ) = 9 + 3 n 3(p + 7 ) = 3 p + 21 2(3 – x ) = 6 – 2 x 3(g – 4 ) = 3 g – 12 5(7 – a ) = 35 – 5 a 2(6 + r ) = 12 + 2 r 9(4 + p ) = 36 + 9 p 8(s – 4 ) = 8 s – 32 3(z – 9 ) = 3 z – 27 4(3 – x + y ) = 12 – 4 x + 4 y © T Madas

“expand” the following brackets: 3(2 a + b ) = 6 a + 3 b 3(2 p – 5 q ) = 6 p – 15 q 2(4 x + 3 ) = 8 x + 6 x (x + 3 ) = x 2 + 3 x 2(3 w + 4 ) = 6 w + 8 u (v + 5 ) = uv + 5 u 3(2 x – 3 y ) = 6 x – 9 y n (3 + m ) = 3 n + nm 4(5 p + 3 ) = 20 p + 12 2 x (4 – x ) = 8 x – 2 x 2 3(3 f – 2 ) = 9 f – 6 b (b – c ) = b 2 – b c 2(4 + 3 a ) = 8 + 6 a 5 r (1 + t ) = 5 r + 5 r t 5(3 c – 7 ) = 15 c – 35 y ( y 2 – 4 ) = y 3 – 4 y © T Madas

“expand” the following brackets: 3(3 b – 4 c ) = 9 b – 12 c 3 e (4 + e ) = 12 e + 3 e 2 p (p + 6 ) = p 2 + 6 p 3 h (4 h + k ) = 12 h 2 + 3 k h x (y + 2 ) = xy + 2 x 2 b (4 a – 5 ) = 8 ab – 10 b v (2 + w ) = 2 v + vw x 2 (2 x + 1 ) = 2 x 3 + x 2 4 t (2 – t ) = 8 t – 4 t 2 3 u (2 u – 5 v ) = 6 u 2 – 15 u v k (k – h ) = k 2 – kh 3 y (2 x – 7 ) = 6 xy – 21 y 3 d (3 + d ) = 9 d + 3 d 2 t 2 (4 t + 3 ) = 4 t 3 + 3 t 2 x (x 2 – 3 ) = x 3 – 3 x p (2 p 2 – 5 q ) = 2 p 3 – 5 pq © T Madas

Which two of the following expressions are equivalent? 5(3 x + 10) 15 x + 50 5 (3 x + 6) 15 x + 30 8(x + 15) 8 x + 120 15(x + 1) 3(5 x + 10) 15 x + 15 15 x + 30 © T Madas

Which of the following expressions are NOT correct factorisations of 24 x + 12? 3(8 x + 4) 2(12 x + 6) 24(x + 2) 12(2 x + 1) 6(4 x + 2) 24 x + 12 24 x + 48 24 x + 12 © T Madas