Activity 7: Find the product of the following: A. Product of two binomials: 1. (2x+3) (4x-5) = 2. (3m +2n) (2m + 3n) = - B. Product of the sum and difference of two terms: : 3. (m +7) (m - 7) = 4. (2x - 5)(2x + 5) = = C. Square of a binomial: 5. (7-5)2 = 6. (x + 3)2 = D. Cube of a binomial: 6.(x+3)3 = E. Product of a binomial and a trinomial: = 7. (2x-3) (4x2 + 6x + 9) = 8. (x+4) (x2 - 4x + 16) =
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Activity 7
A.
1.
(2x + 3)(4x - 5)
= 8x^2 - 10x + 12x - 15
= 8x^2 + 2x - 15
2.
(3m + 2n)(2m + 3n)
= 6m^2 + 6mn + 4mn + 6n^2
= 6m^2 + 6n^2 + 10mn
B.
3.
(m + 7)(m - 7)
= m^2 - 7m + 7m - 49
= m^2 - 49
4.
(2x - 5)(2x + 5)
= 4x^2 + 10x - 10x - 25
= 4x^2 - 25
C.
5.
(y - 5)^2
= (y - 5)(y - 5)
= y^2 - 5y - 5y + 25
= y^2 - 10y + 25
6.
(x + 3)^2
= (x + 3)(x + 3)
= x^2 + 3x + 3x + 9
= x^2 + 6x + 9
D.
6.
(x + 3)^3
= (x + 3)(x + 3)
= x^2 + 3x + 3x + 9
= (x^2 + 6x + 9)(x + 3)
= x^3 + 3x^2 + 6x^2 + 18x + 9x + 27
= x^3 + 9x^2 + 18x + 9x + 27
= x^3 + 9x^2 + 27x + 27
E.
7.
(2x - 3)(4x^2 + 6x + 9)
= 8x^3 + 12x + 18x - 12x^2 - 18x - 27
= 8x^3 + 30x - 12x^2 - 18x - 27
= 8x^3 - 12x^2 + 12x - 27
8.
(x + 4)(x^2 - 4x + 16)
= x^3 - 4x^2 + 16x + 4x^2 - 16x + 64
= x^3 + 16x - 16x + 64
= x^3 - 64
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