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14 (a) Simplify fully $(3x^5y^4)^3$ - Edexcel - GCSE Maths - Question 14 - 2022 - Paper 3

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

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

Step 1

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

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Answer

To simplify the expression ( (3x^5y^4)^3 ), we apply the power of a product rule.

  1. Raise the coefficient to the power: ( 3^3 = 27 ).
  2. For the variable (x): ( (x^5)^3 = x^{15} ).
  3. For the variable (y): ( (y^4)^3 = y^{12} ).

Thus, the simplified expression is:

Final Result: 27x15y12\text{Final Result: } 27x^{15}y^{12}

Step 2

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

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Answer

To expand the expression ( (x + 2y - 3)(x + 4) ), we use the distributive property:

  1. Multiply each term in the first parentheses by each term in the second:

    • ( x \cdot x = x^2 )
    • ( x \cdot 4 = 4x )
    • ( 2y \cdot x = 2xy )
    • ( 2y \cdot 4 = 8y )
    • ( -3 \cdot x = -3x )
    • ( -3 \cdot 4 = -12 )

  2. Combine all the like terms:

    • ( x^2 + (4x - 3x) + 2xy + 8y - 12 )
    • Simplifying, we get: ( x^2 + x + 2xy + 8y - 12 )

Thus, the expanded and simplified expression is:

Final Result: x2+x+2xy+8y−12\text{Final Result: } x^2 + x + 2xy + 8y - 12

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