7. \( x^{4}-x^{2} \) \( 2 \cdot-a^{4}+16 \) \( 3 \cdot \frac{1}{4 b^{2}-\frac{4}{16}} \) \( 4 \cdot(a+x)^{2}-y^{2} \) \( 5 \cdot 81 x^{2}-36 \) \( 6 \cdot 10 b(x-y)+5 \) 7. \( t^{2}(4-t)+4(4-t) \) 8. \( 12 x y^{2}+4 x y-3 x^{3} y^{3} \)

The expression \( x^{4} - x^{2} \) can be factored by recognizing it as a difference of squares: it becomes \( x^{2}(x^{2} - 1) \), which can be further factored to \( x^{2}(x - 1)(x + 1) \). This elegant factoring helps highlight the roots of the equation, which are \( x = 0, -1, 1 \). Another great example is the expression \( 4 \cdot (a+x)^{2} - y^{2} \), which is a difference of squares. This can be factored into \( (2(a+x) - y)(2(a+x) + y) \) using the formula \( A^{2} - B^{2} = (A - B)(A + B) \). This technique often simplifies solving related equations and helps visualize the relationships between variables!