5. Find the product, using suitable properties:
                (a) 26 × (– 48) + (– 48) × (–36)            (b) 8 × 53 × (–125)
                (c) 15 × (–25) × (– 4) × (–10)                (d) (– 41) × 102
                (e) 625 × (–35) + (– 625) × 65             (f) 7 × (50 – 2)
                (g) (–17) × (–29)                                    (h) (–57) × (–19) + 57

Answers (1)

Using suitable properties of multiplication:

(a)

\\ 26 \times (- 48) + (- 48) \times (-36) \\ = (- 48) \times 26 + (- 48) \times (-36)\ \ [a\times b = b\times a] \\ = (- 48) \times [26 + (-36)] \ \ [a\times b + a\times c = a\times(b+c)] \\ = (-48)\times(-10) = 480            

(b)

\\ 8 \times 53 \times (-125) \\ = [8 \times 53 ]\times (-125) \ \[a\times b = b\times a] \\ = 53 \times[ 8 \times (-125)] \ \ a\times(b\times c) =( a\times b)\times c \\ = 53\times(-1000) = -53000                

(c)

\\ 15 \times (-25) \times (- 4) \times (-10) \\ = 15 \times [(-25) \times (- 4)] \times (-10) \\ = 15 \times 100\times (-10) \\ = -15000                

(d)

\\ (- 41) \times 102 \\ =(- 41) \times(100+2) \\ =(- 41) \times100+(- 41) \times2\ \ [a\times(b+c)=(a\times b) + (a\times c)] \\ = (-4100) + (-82) \\ = -4100-82 = -4182                

(e)

\\625 \times (-35) + (- 625) \times 65 \\ = (-625) \times 35 + (- 625) \times 65 \ \[a\times b = b\times a] \\ = (-625) \times (35 +65) \ \ [(a\times b) + (a\times c) = a\times(b+c)] \\ = (-625) \times (100) = -62500

(f)

\\ 7 \times (50 - 2) \\ = (7 \times 50) - (7 \times2) \ \ [a\times(b-c)=(a\times b) - (a\times c)] \\ = 350 -14 = 336
(g)

\\ (-17) \times (-29) \\ =(-17) \times (-30 + 1) \\ = (-17) \times (-30) +(-17) \times 1 \ \ [a\times(b+c)=(a\times b) + (a\times c)] \\ = 510 -17 = 493                                    

(h)

\\ (-57) \times (-19) + 57 \\ = (-57) \times (-19) + (-57) \times(-1) \\ = (-57) \times [(-19) +(-1)] \ \ [(a\times b) + (a\times c) = a\times(b+c)] \\ = (-57) \times (-20) = 1140

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