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... 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 expression, we use the distributive property (FOIL method):
Multiply the first terms: 3x⋅x=3x2.
Multiply the outer terms: 3x⋅y=3xy.
Multiply the inner terms: −2y⋅x=−2xy.
Multiply the last terms: −2y⋅y=−2y2.
Combining these gives:
3x2+3xy−2xy−2y2=3x2+xy−2y2
Thus, the final answer is: 3x2+xy−2y2.
Step 2
Work out the value of c and the value of d.
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Answer
We start with the equation:
3(2x+d)+c(x+5)=10x+17
Expanding the left side, we have:
6x+3d+cx+5c=10x+17
Now we combine like terms:
(6+c)x+(3d+5c)=10x+17
Equating the coefficients for x and the constant term:
For x:
6+c=10
Thus, c=10−6=4.
For the constants:
3d+5c=17
Substituting c=4:
3d+5(4)=173d+20=17
Solving for d:
3d=17−203d=−3
Thus, d=−1.
Step 3
Solve by factorising.
x² - 7x + 10 = 0
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Answer
To solve the quadratic equation by factorisation, we look for two numbers that multiply to 10 and add to -7. The numbers -2 and -5 work:
So we can factor the equation as:
(x−2)(x−5)=0
Setting each factor to zero gives:
