Question

factor completely (x^2-4)(x^2+6x+9)

Answer 1

Answer:

$(x-2)(x+2)\left(x+3\right)^2$  is the required factor form.

Step-by-step explanation:

When the factor of the expression is required to be found, then take the common terms, or find the factor by splitting the terms, or by using the standard formulas.

So here we have to find the factor of the expression:

$(x^2-4)(x^2+6x+9)$

so we will first find the factors of:

$(x^2-4)=(x-2)(x+2)~~~~~~~~~~~~~~~~~\because x^2-y^2=\left(x+y\right)\left(x-y\right)$

Now the factors of:

$(x^2+6x+9)=\left(x+3\right)^2~~~~~~~~~\because \left(a+b\right)^2=a^2+2ab+b^2$

So the final factor is given as:

$(x^2-4)(x^2+6x+9)\\=(x-2)(x+2)\left(x+3\right)^2$