let’s fill up the table below :
let’s fill up the table below :
(b)first part,given, (i) x4 – 4x3 + 6x2(ii) x2(i) × (ii)= (x4 – 4x3 + 6x2) × x2= x4x2 – 4x3x2 + 6x2x2we know (xaxb= xa+b)= x4+2– 4x3+2 + 6x2+2= x6 – 4x5 + 6x4(i) ÷ (ii)we know = x4-2 – 4x3-2 + 6x2-2= x2 – 4x + 6second partgiven, (i) 3m2n3 + 40m3n4 – 5m4n5(ii) 10m2n2(i) × (ii)= (3m2n3 + 40m3n4 – 5m4n5) × 10m2n2we know (xaxb= xa+b)= 30m2m2n3n2 + 400m3m2n4n2 – 50m4m2n5n2= 30m2+2n3+2 + 400m3+2n4+2 – 50m4+2n5+2= 30m4n5 + 400m5n6 – 50m6n7(i) ÷ (ii)we know (c)given,(i) 49l2 – 100m2(ii) (7l + 10m)(i) × (ii)= (49l2 – 100m2)(7l + 10m)we know (xaxb= xa+b)= 343l2l+ 490l2m – 700m2l – 1000m2m= 343l2+1 + 490l2m – 700lm2 – 1000m2+1= 343l3 + 490l2m – 700lm2 – 1000m3(i) ÷ (ii)∵ a2 – b2 = (a – b)(a + b), taking a = 7l, b = 10m we havecancelling out the common terms from numerator and denominator, we get= 7l – 10m(d)given,(i) 625a4 – 81b4(ii) 5a + 3b(i) × (ii)= (625a4 – 81b4)(5a + 3b)= 625a4a + 1875a4b – 405ab4 – 243b4bwe know (xaxb= xa+b)= 625a4+1 + 1875a4b – 405ab4 – 243b4+1= 3125a5 + 1875a4b – 405ab4 – 243b5(i) ÷ (ii)∵ a2 – b2 = (a – b)(a + b), taking a = 25a2, b = 9b2, we have∵ a2 – b2 = (a – b)(a + b), taking a = 5a, b = 3b we have=cancelling out the common terms from numerator and denominator, we get= (5a – 3b)(25a2 + 9b2)= 125aa2 + 45ab2 – 75a2b – 27bb2we know (xaxb= xa+b)= 125a2+1 + 45ab2 – 75a2b – 27b2+1= 125a3 + 45ab2 – 75a2b – 27b3
(b)first part,given, (i) x4 – 4x3 + 6x2(ii) x2(i) × (ii)= (x4 – 4x3 + 6x2) × x2= x4x2 – 4x3x2 + 6x2x2we know (xaxb= xa+b)= x4+2– 4x3+2 + 6x2+2= x6 – 4x5 + 6x4(i) ÷ (ii)we know = x4-2 – 4x3-2 + 6x2-2= x2 – 4x + 6second partgiven, (i) 3m2n3 + 40m3n4 – 5m4n5(ii) 10m2n2(i) × (ii)= (3m2n3 + 40m3n4 – 5m4n5) × 10m2n2we know (xaxb= xa+b)= 30m2m2n3n2 + 400m3m2n4n2 – 50m4m2n5n2= 30m2+2n3+2 + 400m3+2n4+2 – 50m4+2n5+2= 30m4n5 + 400m5n6 – 50m6n7(i) ÷ (ii)we know (c)given,(i) 49l2 – 100m2(ii) (7l + 10m)(i) × (ii)= (49l2 – 100m2)(7l + 10m)we know (xaxb= xa+b)= 343l2l+ 490l2m – 700m2l – 1000m2m= 343l2+1 + 490l2m – 700lm2 – 1000m2+1= 343l3 + 490l2m – 700lm2 – 1000m3(i) ÷ (ii)∵ a2 – b2 = (a – b)(a + b), taking a = 7l, b = 10m we havecancelling out the common terms from numerator and denominator, we get= 7l – 10m(d)given,(i) 625a4 – 81b4(ii) 5a + 3b(i) × (ii)= (625a4 – 81b4)(5a + 3b)= 625a4a + 1875a4b – 405ab4 – 243b4bwe know (xaxb= xa+b)= 625a4+1 + 1875a4b – 405ab4 – 243b4+1= 3125a5 + 1875a4b – 405ab4 – 243b5(i) ÷ (ii)∵ a2 – b2 = (a – b)(a + b), taking a = 25a2, b = 9b2, we have∵ a2 – b2 = (a – b)(a + b), taking a = 5a, b = 3b we have=cancelling out the common terms from numerator and denominator, we get= (5a – 3b)(25a2 + 9b2)= 125aa2 + 45ab2 – 75a2b – 27bb2we know (xaxb= xa+b)= 125a2+1 + 45ab2 – 75a2b – 27b2+1= 125a3 + 45ab2 – 75a2b – 27b3