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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

1 Answer

6 votes
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)
User Andrew Hanson
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