iGCSE Mathematics (0580) : C2.4 Use and interpret positive, negative and zero indices. iGCSE Style Questions Paper 1

Question

Simplify.

(a) $ n^5 \times n $

(b) $ 8x^6 \div 2x^2 $

▶️ Answer/Explanation

Solution

(a) Ans: $ n^6 $

When multiplying with the same base, add the exponents: $ n^5 \times n^1 = n^{5+1} = n^6 $

(b) Ans: $ 4x^4 $

Divide coefficients (8÷2=4) and subtract exponents (6-2=4): $ 4x^{6-2} = 4x^4 $

Question

Factorise completely.

$8x^2-20x$

▶️ Answer/Explanation

Solution

Ans: $4x(2x – 5)$

First, identify the greatest common factor (GCF) of the terms $8x^2$ and $-20x$, which is $4x$.

Next, factor out $4x$ from each term: $8x^2 \div 4x = 2x$ and $-20x \div 4x = -5$.

Thus, the expression factorises to $4x(2x – 5)$.

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