Question

Alyze the following special produ

ve USII
1.
(3x + 5)(2x - 3). Solve using the F.O.I.L.
2.
(x + 2)(x – 13). Solve using the F.O.I.L.
3. (x + 5)2. Solve using the square of Binomial.
1. (x – 3)2 Solve using the square of Binomial.

Answer 1

1) Solving the term
`(3x + 5)(2x - 3)` using F.O.I.L we get
`\mathbf{6x^2+x-15}`

2) solving the term
`(x + 2)(x - 13)` using F.O.I.L we get
`\mathbf{x^2-11x-26}`

3) Solving
`(x+5)^2` using square of binomial we get
`\mathbf{x^2+10x+25}`

4) Solving
`(x+5)^2` using square of binomial we get
`\mathbf{x^2-6x+9}`

Explanation:

1) (3x + 5)(2x - 3). Solve using the F.O.I.L.

F.O.I.L stands for First, Outer Inner Last

We have
`(3x + 5)(2x - 3)`

First: 3x(2x)

Outer: 3x(-3)

Inner: 5(2x)

Last: 5(-3)

Solving we get:

`(3x + 5)(2x - 3)\\=3x(2x)+3x(-3)+5(2x)+5(-3)\\=6x^2-9x+10x-15\\=6x^2+x-15`

So, solving the term
`(3x + 5)(2x - 3)` using F.O.I.L we get
`\mathbf{6x^2+x-15}`

2) (x + 2)(x – 13). Solve using the F.O.I.L.

F.O.I.L stands for First, Outer Inner Last

We have
`(x + 2)(x -13)`

First: x(x)

Outer: x(-13)

Inner: 2(x)

Last: 2(-13)

Solving we get:

`(x + 2)(x - 13)\\=x(x)+x(-13)+2(x)+2(-13)\\=x^2-13x+2x-26\\=x^2-11x-26`

So, solving the term
`(x + 2)(x - 13)` using F.O.I.L we get
`\mathbf{x^2-11x-26}`

3) (x + 5)^2. Solve using the square of Binomial.

The square of binomial is:
`(a+b)^2=a^2+2ab+b^2`

Solving:

`(x+5)^2\\=(x)^2+2(x)(5)+(5)^2\\=x^2+10x+25`

So, solving
`(x+5)^2` using square of binomial we get
`\mathbf{x^2+10x+25}`

4) (x -3)^2. Solve using the square of Binomial.

The square of binomial used is:
`(a-b)^2=a^2-2ab+b^2`

Solving:

`(x-3)^2\\=(x)^2-2(x)(3)+(3)^2\\=x^2-6x+9`

So, solving
`(x+5)^2` using square of binomial we get
`\mathbf{x^2-6x+9}`