Question

Rewrite each algebraic expression in an equivalent form with the fewest

number of terms possible.
a. 6(x + 7)(x + 2)
b. (2y – 5)
c. (5x + 4y)(2x - y)
d. (3x + 7)(3x – 7)
e. (t + 2) – (4t +9) – t

Answer 1

Explanation:

The terms will be multiplied in order to get the simplified polynomials.

a. 6(x + 7)(x + 2)

`6(x + 7)(x + 2)\\=6[x(x+2)+7(x+2)]\\=6(x^2+2x+7x+14)\\=6(x^2+9x+14)\\=6x^2+54x+84`

The simplified form of 6(x + 7)(x + 2) is
`6x^2+54x+84`

b. (2y – 5)^2

Using the formula:
`(a-b)^2 = a^2+b^2-2ab`

`=(2y)^2+(5)^2-2(2y)(5)\\=4y^2+25-20y`

The simplified form is:
`4y^2-20y+25`

c. (5x + 4y)(2x - y)

`=5x(2x-y)+4y(2x-y)\\=10x^2-5xy+8xy-4y^2\\=10x^2+3xy-4y^2`

The simplified form of (5x + 4y)(2x - y) is
`10x^2+3xy-4y^2`

d. (3x + 7)(3x – 7)

Using the formula:
`(a+b)(a-b) = a^2-b^2`

`= (3x)^2-(7)^2\\= 9x^2-49`

The simplified form of (3x + 7)(3x – 7) is
`9x^2-49`

e. (t + 2) – (4t +9) – t

`=t+2-4t-9-t\\=t-4t-t+2-9\\= -4t-7`

The simplified form of (t + 2) – (4t +9) – t is
`-4t-7`

Hence,

a. The simplified form of 6(x + 7)(x + 2) is
`6x^2+54x+84`

b. The simplified form is:
`4y^2-20y+25`

c. The simplified form of (5x + 4y)(2x - y) is
`10x^2+3xy-4y^2`

d. The simplified form of (3x + 7)(3x – 7) is
`9x^2-49`

e. The simplified form of (t + 2) – (4t +9) – t is
`-4t-7`