Question

Replace ∗ with a monomial so that the expression can be rewritten as a square of a sum or a difference:

Answer 1

Answer:

The star * can be replaced by 2bc

Step-by-step explanation:

Square Of A Binomial

The expression $(a+b)^2$ can be expanded as $a^2+2ab+b^2$. Equivalently, if we have the expansion we can reduce to the power of 2. If we know a term is the square of a monomial, we can find the original term by taking the square root.

The given expression is

$0.01b^2+ * + 100c^2$

It's supposed to be the square of a binomial, so we need to test if both of the given terms are perfect squares

$\sqrt{0.01b^2}=0.1b$

$\sqrt{100c^2}=10c$

Once we are sure we have both square terms, we can complete the expression with the remaining part of the expansion, i.e. twice the first by the second term. In other words

$2(0.1b)(10c)=2bc$

The full expression will be

$0.01b^2+ 2bc + 100c^2$

which can be reduced to

$(0.1b+10c)^2$