Question

- 23. Use the identity (x + a)(x + b) = x2 + (a + b)x + ab to find the following products: (a) (2x + 54)(2x + 36) (b) (4x + 5)(4x - 1) 22. Find the square root of the following by the prime factorization method: (a) 4096 (b) 65536 23. Find the cube root of the following by the prime factorization method: (a) 13824 (b) 46656 24. Find the square root by Division method: (a) 5776 (b) 15376 25. Find the value of all the angles in the given triangle if ZX = 3a, _Y = 2a, ZZ = 5a. X Y Z 26. Solve the following word problems: (a) Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers? (b) Three consecutive integers add up to 75. What are these integers? 27. Find the cube root of 103824 hy estimation mothed​

Answer 1

Answer:

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Step-by-step explanation:

a)(x + b) = x2 + (a + b)x + ab to solve the given questions.

(i) (x + 3)(x + 7)

= x2 + (3 + 7)x + (3)(7)

= x2 + 10x + 21

(ii) (4x + 5)(4x + 1)

= (4x)2 + (5 + 1)(4x) + (5)(1)

= 16x2 + 24x + 5

(iii) (4x - 5)(4x - 1)

= (4x)2 + [(-5) + (-1)](4x) + (-5) (-1)

= 16x2 - 24x + 5

(iv) (4x + 5)(4x -1)

= (4x)2 + [(5) + (-1)](4x) + (5)(-1)

= 16x2 + 16x - 5

(v) (2x + 5y)(2x + 3y)

= (2x)2 + (5y + 3y)(2x) + (5y)(3y)

= 4x2 + 16xy + 15y2

(vi) (2a2 + 9)(2a2 + 5)

= (2a2)2 + (9 + 5)(2a2) + (9)(5)

= 4a4 + 28a2 + 45

(vii) (xyz - 4)(xyz - 2)

= (xyz)2 + [(-4) + (-2)](xyz) + (-4)(-2)

= x2y2z2 - 6xyz + 8