Question

Answer 1

a: \(a^2-10a+25-4b^2\)

\(=\left(a-5\right)^2-\left(2b\right)^2\)

=(a-5-2b)(a-5+2b)

b: \(a\left(x^2+1\right)-x\left(a^2+1\right)\)

\(=a\cdot x^2+a-x\cdot a^2-x\)

=ax(x-a)-(x-a)

=(x-a)(ax-1)

c: \(m^3p+m^2np-m^2p^2-mnp^2\)

\(=m^2p\left(n+m\right)-mp^2\left(m+n\right)\)

=mp(m-p)(m+n)

d: \(ab\left(m^2+n^2\right)+mn\left(a^2+b^2\right)\)

\(=ab\cdot m^2+mn\cdot a^2+ab\cdot n^2+mn\cdot b^2\)

=am(bm+an)+bn(an+bm)

=(an+bm)(am+bn)