Use the concept of cube of binomial in solving thefollowing:1. (x - 5) ^ 36. (5x - 6) ^ 32. (y + 3) ^ 37. (x + y) ^ 33. (m + 2) ^ 38. (3p - 4q) ^ 34. (3x + 7) ^ 310. 9.18 (5x + 3y) ^ 3. (2a - 2) ^ 3(3c ^ 2 - 2d) ^ 3what is the answer
Answer (1)
Cube of a Binomial Formula [tex](a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3[/tex]For [tex](a - b)^3[/tex], it becomes: [tex](a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3[/tex]1. [tex](x - 5)^3[/tex][tex]a = x, b = 5[/tex] [tex]= x^3 - 3x^2(5) + 3x(5^2) - 5^3 \\= x^3 - 15x^2 + 75x - 125[/tex]2. [tex](y + 3)^3[/tex][tex]a = y, b = 3[/tex] [tex]= y^3 + 3y^2(3) + 3y(3^2) + 3^3 \\= y^3 + 9y^2 + 27y + 27[/tex]3. [tex](m + 2)^3[/tex][tex]a = m, b = 2[/tex] [tex]= m^3 + 3m^2(2) + 3m(2^2) + 2^3 \\= m^3 + 6m^2 + 12m + 8[/tex]4. [tex](3x + 7)^3[/tex][tex]a = 3x$$, $$b = 7[/tex] [tex]= (3x)^3 + 3(3x)^2(7) + 3(3x)(7^2) + 7^3 \\= 27x^3 + 3 \times 9x^2 \times 7 + 3 \times 3x \times 49 + 343 \\= 27x^3 + 189x^2 + 441x + 343[/tex]5. [tex](5x - 6)^3[/tex][tex]a = 5x$$, $$b = 6[/tex] (sign negative) [tex]= (5x)^3 - 3(5x)^2(6) + 3(5x)(6^2) - 6^3 \\= 125x^3 - 3 \times 25x^2 \times 6 + 3 \times 5x \times 36 - 216 \\= 125x^3 - 450x^2 + 540x - 216[/tex]6. [tex]$$(x + y)^3[/tex][tex]a = x$$, $$b = y[/tex] [tex]= x^3 + 3x^2y + 3xy^2 + y^3[/tex]7. [tex]$$(3p - 4q)^3[/tex][tex]a = 3p$$, $$b = 4q[/tex] (sign negative) [tex]= (3p)^3 - 3(3p)^2(4q) + 3(3p)(4q)^2 - (4q)^3 \\= 27p^3 - 3 \times 9p^2 \times 4q + 3 \times 3p \times 16q^2 - 64q^3 \\= 27p^3 - 108p^2q + 144pq^2 - 64q^3[/tex]8. [tex]$$(5x + 3y)^3[/tex][tex]a = 5x$$, $$b = 3y[/tex] [tex]= (5x)^3 + 3(5x)^2(3y) + 3(5x)(3y)^2 + (3y)^3 \\= 125x^3 + 3 \times 25x^2 \times 3y + 3 \times 5x \times 9y^2 + 27y^3 \\= 125x^3 + 225x^2y + 135xy^2 + 27y^3[/tex]9. [tex]$$(2a - 2)^3[/tex][tex]a = 2a$$, $$b = 2[/tex] (sign negative) [tex]= (2a)^3 - 3(2a)^2(2) + 3(2a)(2^2) - 2^3 \\= 8a^3 - 3 \times 4a^2 \times 2 + 3 \times 2a \times 4 - 8 \\= 8a^3 - 24a^2 + 24a - 8[/tex]10. [tex]$$(3c^2 - 2d)^3[/tex][tex]a = 3c^2$$, $$b = 2d[/tex] [tex]= (3c^2)^3 - 3(3c^2)^2(2d) + 3(3c^2)(2d)^2 - (2d)^3 \\= 27c^6 - 3 \times 9c^4 \times 2d + 3 \times 3c^2 \times 4d^2 - 8d^3 \\= 27c^6 - 54c^4 d + 36 c^2 d^2 - 8 d^3[/tex]
