Question

Answer this in pattern,show the solution

Cube of Binomial

1.) (x+4)³
2.) (x-4)³
3.) (7m-3n)³
4.) (3xy+1)

Factoring:Factor the ff. Trinomials

1.) 6m³-9m²
2.) 6m²-12mn²+3n

Factor the difference of two square

1.) 9x²-25y²
2.)36x²-49y²
3.)32m²-98n²
4.)36p²-25

Answer 1

Cube of Binomial
1.$(x + 4)^{3}$
   $(x + 4)(x + 4)(x + 4)$
   $(x(x + 4) + 4(x + 4))(x + 4)$
   $(x(x) + x(4) + 4(x) + 4(4))(x + 4)$
   $(x^{2} + 4x + 4x + 16)(x + 4)$
   $(x^{2} + 8x + 16)(x + 4)$
   $x^{2}(x + 4) + 8x(x + 4) + 16(x + 4)$
   $x^{2}(x) + x^{2}(4) + 8x(x) + 8x(4) + 16(x) + 16(4)$
   $x^{3} + 4x^{2} + 8x^{2} + 32x + 16x + 64$
   $x^{3} + 12x^{2} + 48x+ 64$

2.$(x - 4)^{3}$
   $(x - 4)(x - 4)(x - 4)$
   $(x(x - 4) - 4(x - 4))(x - 4)$
   $(x(x) - x(4) - 4(x) + 4(4))(x - 4)$
   $(x^{2} - 4x - 4x + 16)(x - 4)$
   $(x^{2} - 8x + 16)(x - 4)$
   $x^{2}(x - 4) - 8x(x - 4) + 16(x - 4)$
   $x^{2}(x) - x^{2}(4) - 8x(x) + 8x(4) + 16(x) - 16(4)$
   $x^{3} - 4x^{2} - 8x^{2} + 32x + 16x - 64$
   $x^{3} - 12x^{2} + 48x - 64$

3.$(7m - 3n)^{3}$
   $(7m - 3n)(7m - 3n)(7m - 3n)$
   $(7m(7m - 3n) - 3n(7m - 3n))(7m - 3n)$
   $(7m(7m) - 7m(3n) - 3n(7m) + 3n(3n))(7m - 3n)$
   $(49m^{2} - 21mn - 21mn + 9n^{2})(7m - 3n)$
   $(49m^{2} - 42mn + 9n^{2})(7m - 3n)$
   $49m^{2}(7m - 3n) - 42mn(7m - 3n) + 9n^{2}(7m - 3n)$
   $49m^{2}(7m) - 49m^{2}(3n) - 42mn(7m) + 42mn(3n) + 9n^{2}(7m) - 9n^{2}(3n)$
   $343m^{3} - 147m^{2}n - 294m^{2}n + 126mn^{2} + 63mn^{2} - 27n^{3}$
   $343m^{3} - 441m^{2}n + 189mn^{2} - 27n^{3}$

4.$(3xy + 1)^{3}$
   $(3xy + 1)(3xy + 1)(3xy + 1)$
   $(3xy(3xy + 1) + 1(3xy + 1))(3xy + 1)$
   $(3xy(3xy) + 3xy(1) + 1(3xy) + 1(1))(3xy + 1)$
   $(9x^{2}y^{2} + 3xy + 3xy + 1)(3xy + 1)$
   $(9x^{2}y^{2} + 6xy + 1)(3xy + 1)$
   $9x^{2}y^{2}(3xy + 1) + 6xy(3xy + 1) + 1(3xy + 1)$
   $9x^{2}y^{2}(3xy) + 9x^{2}y^{2}(1) + 6xy(3xy) + 6xy(1) + 1(3xy) + 1(1)$
   $27x^{3}y^{3} + 9x^{2}y^{2} + 18x^{2}y^{2} + 6xy + 3xy + 1$
   $27x^{3}y^{3} + 27x^{2}y^{2} + 9xy + 1$

Factoring Trinomials
1.$6m^{3} - 9m^{2}$
   $3m^{2}(2m) + 3m^{2}(3)$
   $3m^{2}(2m + 3)$

2.$6m^{2} - 12mn^{2} + 3n$
   $3(2m^{2}) - 3(4mn^{2}) + 3(n)$
   $3(2m^{2} - 4mn^{2} + n)$

Factoring the Difference of Two Squares
1.$9x^{2} - 25y^{2}$
   $9x^{2} + 15xy - 15xy - 25y^{2}$
   $3x(3x) + 3x(5y) - 5y(3x) - 5y(5y)$
   $3x(3x + 5y) - 5y(3x + 5y)$
   $(3x - 5y)(3x + 5y)$

2.$36x^{2} - 49y^{2}$
   $36x^{2} - 42xy + 42xy - 49y^{2}$
   $6x(6x) - 6x(7y) + 7y(6x) - 7y(7x)$
   $6x(6x - 7y) + 7y(6x - 7y)$
   $(6x + 7y)(6x - 7y)$

3.$32m^{2} - 98n^{2}$
   $2(16m^{2}) - 2(49n^{2})$
   $2(16m^{2} - 49n^{2})$
   $2(16m^{2} - 28mn + 28mn - 49n^{2})$
   $2(4m(4m) - 4m(7n) + 7n(4m) - 7n(7n))$
   $2(4m(4m - 7n) + 7n(4m - 7n))$
   $2(4m + 7n)(4m - 7n)$

4.$36p^{2} - 25$
   $36p^{2} - 30p + 30p - 25$
   $6p(6p) - 6p(5) + 5(6p) - 5(5)$
   $6p(6p - 5) + 5(6p - 5)$
   $(6p + 5)(6p - 5)$