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14 (a) Simplify fully $(3x^5y^4)$ (b) Expand and simplify $(x + 2y - 3)(x + 4)$ - Edexcel - GCSE Maths - Question 14 - 2022 - Paper 3

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14-(a)-Simplify-fully--$(3x^5y^4)$--(b)-Expand-and-simplify-$(x-+-2y---3)(x-+-4)$-Edexcel-GCSE Maths-Question 14-2022-Paper 3.png

14 (a) Simplify fully $(3x^5y^4)$ (b) Expand and simplify $(x + 2y - 3)(x + 4)$

Worked Solution & Example Answer:14 (a) Simplify fully $(3x^5y^4)$ (b) Expand and simplify $(x + 2y - 3)(x + 4)$ - Edexcel - GCSE Maths - Question 14 - 2022 - Paper 3

Step 1

Simplify fully $(3x^5y^4)$

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Answer

To simplify the expression (3x5y4)(3x^5y^4) fully, we observe that it is already in its simplest form. However, we can state it as:

3x5y43x^5y^4.

Step 2

Expand and simplify $(x + 2y - 3)(x + 4)$

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Answer

To expand and simplify the expression (x+2y−3)(x+4)(x + 2y - 3)(x + 4), we can use the distributive property (also known as the FOIL method for binomials).

  1. Distribute each term in the first polynomial by each term in the second polynomial:

    (x)(x)+(x)(4)+(2y)(x)+(2y)(4)−(3)(x)−(3)(4)(x)(x) + (x)(4) + (2y)(x) + (2y)(4) - (3)(x) - (3)(4)

    This results in:

    x2+4x+2xy+8y−3x−12x^2 + 4x + 2xy + 8y - 3x - 12

  2. Now, combine like terms:

    x2+(4x−3x)+2xy+8y−12x^2 + (4x - 3x) + 2xy + 8y - 12

    which simplifies to:

    x2+xy+8y−12x^2 + xy + 8y - 12.

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