Expanding triple brackets

The Maths Habit

  1. Expand and simplify (x + 5)(x + 2)

    x2 + 7x + 10

  2. Expand and simplify (x − 4)(x + 9)

    x2 + 5x − 36

  3. Expand and simplify (y − 3)(y − 7)

    y2 − 10y + 21

Which is bigger?
Decide without working them out.

11 × 12 × 13   or   12 × 12 × 12

12 × 12 × 12, by 12

Work out

  1. x × x

    x2

  2. x × x2

    x3

  3. 3 × 2x

    6x

  4. −3 × 4x

    −12x

Expand and simplify (x + 1)(x + 3)(x + 4)

the first two brackets
×x+3
xx23x
+1x3
=x2 + 4x + 3
then multiply by the third
×x2+4x+3
xx34x23x
+44x216x12
Answerx3 + 8x2 + 19x + 12

Expand and simplify (x + 1)(x + 1)(x + 3)

the first two brackets
×x+1
xx2x
+1x1
=x2 + 2x + 1
then multiply by the third
×x2+2x+1
xx32x2x
+33x26x3
Answerx3 + 5x2 + 7x + 3

Expand and simplify (x + 1)(x + 3)(x + 4)

the first two brackets
×x+3
xx23x
+1x3
=x2 + 4x + 3
then multiply by the third
×x2+4x+3
xx34x23x
+44x216x12
Answerx3 + 8x2 + 19x + 12

Expand and simplify (x + 2)(x + 4)(x − 3)

the first two brackets
×x+4
xx24x
+2x8
=x2 + 6x + 8
then multiply by the third
×x2+6x+8
xx36x28x
−3−3x2−18x−24
Answerx3 + 3x2 − 10x − 24

Expanding triple brackets worksheet, page 1

Answer sheet

  1. Expand and simplify (x + 2)3

    x3 + 6x2 + 12x + 8

  2. A cuboid measures x, x + 1 and x + 4. Find an expression for its volume.

    x3 + 5x2 + 4x

  1. Expand and simplify (x + 1)(x + 2)(x + 5)

    x3 + 8x2 + 17x + 10

  2. Expand and simplify (x + 3)(x − 2)(x + 4)

    x3 + 5x2 − 2x − 24

  3. Kit says (x − 1)3 = x3 − 1. Find the right answer.

    x3 − 3x2 + 3x − 1
Exit tickets to print