Question

Alyze the following special produ

Answer 1

Answer:

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 $\mathbf{x^2-6x+9}$

Step-by-step 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 $\mathbf{x^2-6x+9}$