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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) S... 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)
Answer
To multiply out the expression, use the distributive property:
-
Distribute each term in the first bracket by each term in the second bracket:
egin{align*} (3x - 2y)(x + y) & = 3x imes x + 3x imes y - 2y imes x - 2y imes y
& = 3x^2 + 3xy - 2xy - 2y^2
& = 3x^2 + (3 - 2)xy - 2y^2
& = 3x^2 + xy - 2y^2.
ext{Final answer: } 3x^2 + xy - 2y^2
\end{align*}
Step 2
3(2x + d) + c(x + 5) = 10x + 17
Answer
To solve for c and d:
-
Expand the left-hand side:
egin{align*} 3(2x + d) + c(x + 5) & = 6x + 3d + cx + 5c
& = (6 + c)x + (3d + 5c).
ext{Set equal to } 10x + 17:
(6 + c)x + (3d + 5c) = 10x + 17.
ext{This gives us two equations:}
6 + c = 10
3d + 5c = 17.
2. Solve for c:
c = 10 - 6 = 4.
3. Substitute c into the second equation:
3d + 5(4) = 17
3d + 20 = 17
3d = 17 - 20
3d = -3
d = -1.
ext{Final values: } c = 4, d = -1 \end{align*}
Step 3
Solve by factorising. x² - 7x + 10 = 0
Answer
To solve the equation by factorising:
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Look for two numbers that multiply to 10 (the constant term) and add to -7 (the coefficient of x).
The numbers -2 and -5 work since:
-2 * -5 = 10
-2 + -5 = -7. -
Write the factorised form:
(x - 2)(x - 5) = 0.
-
Set each factor to zero:
x - 2 = 0 ⟹ x = 2
x - 5 = 0 ⟹ x = 5. -
The final solutions are:
x = 2
x = 5.