15
(a) Multiply out - OCR - GCSE Maths - Question 15 - 2018 - Paper 2
Question 15
15
(a) Multiply out.
(3x - 2y)(x + y)
Give your answer in its simplest form.
(b) 3(2x + d) + c(x + 5) = 10x + 17
Work out the value of c and the value of d.
(c... show full transcript
Worked Solution & Example Answer:15
(a) Multiply out - OCR - GCSE Maths - Question 15 - 2018 - Paper 2
Step 1
Multiply out.
(3x - 2y)(x + y)
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Answer
To multiply the two binomials, we apply the distributive property:
First, multiply the first term of the first binomial by both terms of the second:
3x⋅x=3x2
3x⋅y=3xy
Next, multiply the second term of the first binomial by both terms of the second:
−2y⋅x=−2xy
−2y⋅y=−2y2
Now, combine all these results:
3x2+3xy−2xy−2y2
Finally, simplify by combining like terms:
3x2+(3xy−2xy)−2y2=3x2+xy−2y2
Thus, the final answer in simplest form is:
3x2+xy−2y2
Step 2
Work out the value of c and the value of d.
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Answer
To solve the equation:
3(2x+d)+c(x+5)=10x+17
Expand the left-hand side:
6x+3d+cx+5c=10x+17
Combine like terms:
Grouping x terms: (6+c)x+(3d+5c)=10x+17
From the equation, we can deduce the coefficients:
For the x terms: 6+c=10 gives us:
c=10−6=4
For the constant terms: 3d+5c=17:
Substitute c=4:
3d+20=17
This simplifies to:
3d=17−20=−3;
Therefore, d=−1
Thus, the values are:
c=4
d=−1
Step 3
Solve by factorising.
x² - 7x + 10 = 0
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Answer
To solve the quadratic equation by factorising, we need to find two numbers that multiply to 10 and add up to -7.
The two numbers that satisfy these conditions are -5 and -2.
Therefore, we can factorise the quadratic as:
(x−5)(x−2)=0
Setting each factor to zero provides the solutions:
