Photo AI

Expand and simplify $(x - 2)(x^2 + 2x + 3)$ (Total for Question 12 is 3 marks) - Edexcel - GCSE Maths - Question 13 - 2021 - Paper 2

Question icon

Question 13

Expand-and-simplify-$(x---2)(x^2-+-2x-+-3)$--(Total-for-Question-12-is-3-marks)-Edexcel-GCSE Maths-Question 13-2021-Paper 2.png

Expand and simplify $(x - 2)(x^2 + 2x + 3)$ (Total for Question 12 is 3 marks)

Worked Solution & Example Answer:Expand and simplify $(x - 2)(x^2 + 2x + 3)$ (Total for Question 12 is 3 marks) - Edexcel - GCSE Maths - Question 13 - 2021 - Paper 2

Step 1

Expand the expression

96%

114 rated

Answer

To expand the expression, we apply the distributive property (also known as the FOIL method for binomials).

the expression can be expanded as follows:

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

Calculating each part:

  1. For the first term: x(x2+2x+3)=x3+2x2+3xx(x^2 + 2x + 3) = x^3 + 2x^2 + 3x

  2. For the second term: −2(x2+2x+3)=−2x2−4x−6-2(x^2 + 2x + 3) = -2x^2 - 4x - 6

Now we combine these results:

x3+2x2+3x−2x2−4x−6x^3 + 2x^2 + 3x - 2x^2 - 4x - 6.

Step 2

Combine like terms

99%

104 rated

Answer

Now we simplify by combining like terms:

  • The x2x^2 terms: ( 2x^2 - 2x^2 = 0 )
  • The xx terms: ( 3x - 4x = -x )
  • The constant term remains: ( -6 )

Thus, the simplified expression is:

x3−x−6 x^3 - x - 6

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;