Use the formula a (b + c) = a × b + a × c to carry out the following multiplication:

(1) 51 × 51
(2) 75 × 75
(3) 102 × 102

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Solution

(1) 51 × 51 can be expressed as:
51 × (50 + 1)
= 51 × 50 + 51 × 1 (using a × (b + c) = a × b + a × c)
= 2550 + 51
= 2601

(2) 75 × 75 can be expressed as:
75 × (50 + 25)
= 75 × 50 + 75 × 25 (using a × (b + c) = a × b + a × c)
= 3750 + 1875
= 5625

(3) 102 × 102 can be expressed as:
102 × (100 + 2)
= 102 × 100 + 102 × 2 (using a × (b + c) = a × b + a × c)
= 10200 + 204
= 10404

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A = [\begin{matrix} 1 & - 1 \\ 0 & 2 \end{matrix}], B = [\begin{matrix} - 1 & 0 \\ 2 & 1 \end{matrix}] and C = [\begin{matrix} 0 & 1 \\ 1 & - 1 \end{matrix}]

A = [\begin{matrix} 2 & - 1 \\ 1 & 1 \\ - 1 & 2 \end{matrix}], B = [\begin{matrix} 0 & 1 \\ 1 & 1 \end{matrix}] and C = [\begin{matrix} 1 & - 1 \\ 0 & 1 \end{matrix}] .

Question 42

If AB + 7C = 102, Where B $\neq$ 0, C $\neq$ 0, then A + B + C = 14.

(x + a) (x + b) = x^{2} + (a + b) + a b

102 \times 99

C_{0}^{2} + 3 C_{1}^{2} + 5 C_{2}^{2} + \dots

51

C_{r} =^{50} C_{r}

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