Question

multiplying binomials using property
read the section below and complete the following activity (adapted from lesson
recall that a binomial is a polynomial with two terms. when we multiply a binomial with anothe
must distribute twice to complete the multiplication. this process is very similar to using a table.
polynomial will have at most four terms, which may simplify to fewer terms if like terms are present.
examples multiply by using the distributive property.
a. $(a + 3)(a + 10)$
$(a + 3)\overline{(a + 10)} = a(a + 10) + 3(a + 10)$ use the distributive property
$= a^2 + 10a + 3a + 30$ use the distributive property
$= a^2 + 13a + 30$ combine like terms
b. $(4x - 6)(x - 5)$
$(4x + 6)\overline{(x - 5)} = 4x(x - 5) - 6(x - 5)$ use the distributive property
$= 4x^2 - 20x - 6x + 30$ use the distributive property
$= 4x^2 - 26x + 30$ combine like terms
c. $(3q - 5r)(4q + 3r)$
$(3q - 5r)\overline{(4q + 3r)} = 3q(4q + 3r) - 5r(4q + 3r)$ use the distributive property
$= 12q^2 + 9qr - 20qr - 15r^2$ use the distributive property
$= 12q^2 - 11qr - 15r^2$ combine like terms

multiply by using the distributive property.

1. $(d + 8)(d - 4)$
2. $(x - 5)(x - 5)$
3. $(5b + 1)(b - 2)$
4. $(2m - 5)(3m + 8)$

Explanation:

Problem 1: $(d + 8)(d - 4)$

Step1: Apply Distributive Property

$(d + 8)(d - 4) = d(d - 4) + 8(d - 4)$

Step2: Distribute again

$= d^2 - 4d + 8d - 32$

Step3: Combine like terms

$= d^2 + 4d - 32$

Problem 2: $(x - 5)(x - 5)$

Step1: Apply Distributive Property

$(x - 5)(x - 5) = x(x - 5) - 5(x - 5)$

Step2: Distribute again

$= x^2 - 5x - 5x + 25$

Step3: Combine like terms

$= x^2 - 10x + 25$

Problem 3: $(5b + 1)(b - 2)$

Step1: Apply Distributive Property

$(5b + 1)(b - 2) = 5b(b - 2) + 1(b - 2)$

Step2: Distribute again

$= 5b^2 - 10b + b - 2$

Step3: Combine like terms

$= 5b^2 - 9b - 2$

Problem 4: $(2m - 5)(3m + 8)$

Step1: Apply Distributive Property

$(2m - 5)(3m + 8) = 2m(3m + 8) - 5(3m + 8)$

Step2: Distribute again

$= 6m^2 + 16m - 15m - 40$

Step3: Combine like terms

$= 6m^2 + m - 40$

Answer:

1. $\boldsymbol{d^2 + 4d - 32}$
2. $\boldsymbol{x^2 - 10x + 25}$
3. $\boldsymbol{5b^2 - 9b - 2}$
4. $\boldsymbol{6m^2 + m - 40}$