Question

Expand $(x-4)(x+4)(x-3)(x+3)$

Answer 1

Using the identity is $(x+y)(x-y)=x^2-y^2$.

Consider $(x-4)(x+4)(x-3)(x+3)$ we apply the above identity as follows:

$(x-4)(x+4)(x-3)(x+3)=[{\left(x\right)}^2-{\left(4\right)}^2][{\left(x\right)}^2-{\left(3\right)}^2]=(x^2-16)(x^2-9)$

Also we know the identity is $(x-a)(x-b)=x^2-x(a+b)+ab$.

We have, $(x^2-16)(x^2-9)$ , apply the above identity as follows:

$(x^2-16)(x^2-9)={\left(x^2\right)}^2-\left(x^2\right)(16+9)+(16\times 9)=x^4-25x^2+144$

Hence, $(x-4)(x+4)(x-3)(x+3)=x^4-25x^2+144$.