Pythagorist
Algebra

Expanding Brackets Calculator

Expand single brackets, double brackets using the FOIL method, or difference of two squares expressions — with full step-by-step working. Ideal for GCSE algebra and A-level revision.

Format: (ax + b)(cx + d)

Expanding: (1x +4)(1x -3)

Expanded form

1x² +1x -12

How it works

  1. Write the expression

    (1x+4)(1x−3)(1x +4)(1x -3)

    Expand using the FOIL method: First, Outer, Inner, Last.

  2. First — multiply the first terms

    1x×1x=1x21x \times 1x = 1x^2

    First: 1x × 1x = 1x².

    Result:1x²

  3. Outer — multiply the outer terms

    1x×−3=−3x1x \times -3 = -3x

    Outer: 1x × -3 = -3x.

    Result:-3x

  4. Inner — multiply the inner terms

    4×1x=4x4 \times 1x = 4x

    Inner: 4 × 1x = 4x.

    Result:4x

  5. Last — multiply the last terms

    4×−3=−124 \times -3 = -12

    Last: 4 × -3 = -12.

    Result:-12

  6. Collect like terms

    1x2+(−3x+4x)+−12=1x2+1x−121x^2 + (-3x + 4x) + -12 = 1x^2 +1x -12

    Combine the x terms: -3x + 4x = 1x. Final answer: 1x² +1x -12.

    Result:1x² +1x -12

FOIL method for double brackets

(ax+b)(cx+d)=acx2+(ad+bc)x+bd(ax + b)(cx + d) = acx^2 + (ad + bc)x + bd
FFFirst: ax × cx = acx²
OOOuter: ax × d = adx
IIInner: b × cx = bcx
LLLast: b × d = bd

Example substitution

(x+3)(x−2)=x2−2x+3x−6=x2+x−6(x + 3)(x - 2) = x^2 - 2x + 3x - 6 = x^2 + x - 6

F: x×x = x². O: x×(−2) = −2x. I: 3×x = 3x. L: 3×(−2) = −6. Collect: x² + x − 6.

Worked examples

Expand 3(2x + 5)

  1. 1
    3 × 2x: = 6x
  2. 2
    3 × 5: = 15
Answer: 6x + 15

Expand (x + 3)(x + 4)

  1. 1
    First: x × x = x²
  2. 2
    Outer: x × 4 = 4x
  3. 3
    Inner: 3 × x = 3x
  4. 4
    Last: 3 × 4 = 12
  5. 5
    Collect: x² + 7x + 12
Answer: x² + 7x + 12

Expand (x + 5)(x − 5)

  1. 1
    Difference of squares: (a+b)(a−b) = a² − b²
  2. 2
    Apply: x² − 25
Answer: x² − 25

Frequently asked questions

How do you expand single brackets?+

Multiply the term outside the bracket by every term inside. E.g., 3(x + 4) = 3x + 12.

How do you expand double brackets?+

Use FOIL: multiply the First, Outer, Inner, Last terms. E.g., (x+2)(x+3) = x²+3x+2x+6 = x²+5x+6.

What is the difference of two squares?+

(a+b)(a−b) = a²−b². This special case has no middle term.

How do you expand (x+3)²?+

(x+3)² = (x+3)(x+3) = x²+6x+9.

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