What is the simplest form of this binomial expression? a4 − b4

Question

What is the simplest form of this binomial expression?

a4 − b4

0

Answers ( No )

    0
    2021-09-06T06:24:16+00:00

    Answer and work in images

    0
    2021-09-06T06:24:30+00:00

    Answer:

    a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})

    Step-by-step explanation:

    The given expression is

    a^{4}-b^{4}

    This expression is the difference of two perfect squares, and their square roots are

    \sqrt{a^{4}} =a^{2}\\  \sqrt{b^{4}} =b^{2}

    Now, the difference of two perfect squares can be factored as

    x^{2} -y^{2}=(x+y)(x-y)

    So, if we apply this rule, the result would be

    a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})

    Therefore, the simplest form of the binomial expression is

    a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})

Leave an answer

Browse
Browse