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Solve. $$x^2 - 6x + 15 = 3x - 5$$ Expand and simplify - OCR - GCSE Maths - Question 13 - 2017 - Paper 1

Question 13

Solve. $$x^2 - 6x + 15 = 3x - 5$$ Expand and simplify. $$(2x - 1)(x + 5)(3x - 2)$$

Worked Solution & Example Answer:Solve. $$x^2 - 6x + 15 = 3x - 5$$ Expand and simplify - OCR - GCSE Maths - Question 13 - 2017 - Paper 1

Step 1

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Answer

First, rearrange the equation to one side:

$x^2 - 6x + 15 - 3x + 5 = 0$

Combine like terms:

$x^2 - 9x + 20 = 0$

Next, factor the quadratic equation:

$(x - 4)(x - 5) = 0$

Setting each factor to zero gives:

$x - 4 = 0 \Rightarrow x = 4$ $x - 5 = 0 \Rightarrow x = 5$

Thus, the solutions are: $x = 4$ or $x = 5$ .

Step 2

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Answer

First, expand the first two binomials:

$(2x - 1)(x + 5) = 2x^2 + 10x - x - 5 = 2x^2 + 9x - 5$

Now, multiply this result by the third binomial:

$(2x^2 + 9x - 5)(3x - 2)$

Expanding this:

$= 2x^2 \cdot 3x + 2x^2 \cdot (-2) + 9x \cdot 3x + 9x \cdot (-2) - 5 \cdot 3x - 5 \cdot (-2)$

$= 6x^3 - 4x^2 + 27x - 18 - 15x + 10$

Combining like terms gives:

$6x^3 + (-4x^2) + (27x - 15x) + 10 - 18$

$= 6x^3 - 4x^2 + 12$ .

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