6. (a) Simplify fully - OCR - GCSE Maths - Question 6 - 2017 - Paper 1
Question 6
6. (a) Simplify fully.
(i) 4(c + 2d) + 3(3c - 5d)
(ii) 4a × 5b
(b) Factorise fully.
(i) 6g + 8h
(ii) 5x² - 15x
Worked Solution & Example Answer:6. (a) Simplify fully - OCR - GCSE Maths - Question 6 - 2017 - Paper 1
Simplify fully.
(i) 4(c + 2d) + 3(3c - 5d)
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To simplify the expression, we start by distributing the constants into the brackets:
-
Multiply out the terms:
4(c + 2d) &= 4c + 8d, \
3(3c - 5d) &= 9c - 15d.
\\
ext{So the expression becomes:} \
4c + 8d + 9c - 15d.
\\
2. Combine like terms:
\
(4c + 9c) + (8d - 15d) = 13c - 7d.
\\
ext{Thus, the simplified result is:}
\boxed{13c - 7d}.
\end{aligned}$$
Simplify fully.
(ii) 4a × 5b
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To simplify the expression:
-
Multiply the coefficients and the variables separately:
4a×5b=(4×5)(a×b)=20ab.
ext{Thus, the final answer is:}
\boxed{20ab}.
Factorise fully.
(i) 6g + 8h
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To factorise the expression:
-
Identify the greatest common factor (GCF) of the terms:
The GCF of 6g and 8h is 2.
-
Factor out the GCF:
6g+8h=2(3g+4h).
ext{Therefore, the factorised form is:}
\boxed{2(3g + 4h)}.
Factorise fully.
(ii) 5x² - 15x
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To factorise the expression:
-
Identify the greatest common factor (GCF):
The GCF of 5x² and -15x is 5x.
-
Factor out the GCF:
5x2−15x=5x(x−3).
ext{Thus, the factorised form is:}
\boxed{5x(x - 3)}.
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