Expanding binomials Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Expanding binomials questions. See exactly how to solve problems on expanding double brackets, FOIL, squaring a binomial, perfect square.

expanding double bracketsFOILsquaring a binomialperfect squaredifference of two squaresnegative terms
GCSE Foundation70 questionsStep-by-step solutions
Question 1
2 markseasy
Which of the following is the correct expansion of (x+2)(x+3)(x + 2)(x + 3)?

Worked solution

  1. Set up the expansion (FOIL)

    (x+2)(x+3)(x + 2)(x + 3)

    Every term in the first bracket must be multiplied by every term in the second.

  2. Multiply out the pairs

    =x2+3x+2x+6= x^2 + 3x + 2x + 6

    Multiply the First, Outer, Inner and Last terms to get four terms.

  3. Collect like terms

    =x2+5x+6= x^2 + 5x + 6

    Combine the x-terms 3x and 2x to get 5x.

Answer
x2+5x+6x^2 + 5x + 6
Question 2
2 markseasy
Expand and simplify (x+1)(x+2)(x + 1)(x + 2).

Worked solution

  1. Set up the expansion (FOIL)

    (x+1)(x+2)(x + 1)(x + 2)

    Every term in the first bracket must be multiplied by every term in the second.

  2. Multiply out the pairs

    =x2+2x+x+2= x^2 + 2x + x + 2

    Multiply the First, Outer, Inner and Last terms to get four terms.

  3. Collect like terms

    =x2+3x+2= x^2 + 3x + 2

    Combine the x-terms 2x and x to get 3x.

Answer
x2+3x+2x^2 + 3x + 2
Question 3
2 markseasy
Expand and simplify (x+1)(x+4)(x + 1)(x + 4).

Worked solution

  1. Set up the expansion (FOIL)

    (x+1)(x+4)(x + 1)(x + 4)

    Every term in the first bracket must be multiplied by every term in the second.

  2. Multiply out the pairs

    =x2+4x+x+4= x^2 + 4x + x + 4

    Multiply the First, Outer, Inner and Last terms to get four terms.

  3. Collect like terms

    =x2+5x+4= x^2 + 5x + 4

    Combine the x-terms 4x and x to get 5x.

Answer
x2+5x+4x^2 + 5x + 4
Question 4
2 markseasy
Expand and simplify (x+3)(x+4)(x + 3)(x + 4).

Worked solution

  1. Set up the expansion (FOIL)

    (x+3)(x+4)(x + 3)(x + 4)

    Every term in the first bracket must be multiplied by every term in the second.

  2. Multiply out the pairs

    =x2+4x+3x+12= x^2 + 4x + 3x + 12

    Multiply the First, Outer, Inner and Last terms to get four terms.

  3. Collect like terms

    =x2+7x+12= x^2 + 7x + 12

    Combine the x-terms 4x and 3x to get 7x.

Answer
x2+7x+12x^2 + 7x + 12
Question 5
2 markseasy
Expand and simplify (x+2)(x+5)(x + 2)(x + 5).

Worked solution

  1. Set up the expansion (FOIL)

    (x+2)(x+5)(x + 2)(x + 5)

    Every term in the first bracket must be multiplied by every term in the second.

  2. Multiply out the pairs

    =x2+5x+2x+10= x^2 + 5x + 2x + 10

    Multiply the First, Outer, Inner and Last terms to get four terms.

  3. Collect like terms

    =x2+7x+10= x^2 + 7x + 10

    Combine the x-terms 5x and 2x to get 7x.

Answer
x2+7x+10x^2 + 7x + 10

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