Notice that 25z²–16 is a difference of squares, because it can be written in the form a²–b², where a is 5z and b is 4.

a²–b²

(5z)²–4²

25z²–16

Now use the formula for factorising a difference of squares.

a²–b²=(a+b)(a–b)

(5z)²–4²=(5z+4)(5z–4)

25z²–16=(5z+4)(5z–4)

The factorised form of 25z²–16 is (5z+4)(5z–4).

Finally, check your work.

(5z+4)(5z–4)

25z²+20z–20z–16Apply the distributive property (FOIL)

25z²–16

Yes, 25z²–16=(5z+4)(5z–4).

Notice that f²–8f+16 is a perfect square trinomial because it can be written in the form a²–2ab+b², where a is f and b is 4.

a²–2ab+b²

f²–2f . 4+4²

f²–8f+16

Now use the formula for factorising perfect square trinomials.

a²–2ab+b²=(a–b)²

f²–2f . 4+4²=(f–4)²

f²–8f+16=(f–4)²

The factorised form of f²–8f+16 is (f–4)².

Finally, check your work.

(f–4)²

(f–4)(f–4)Expand

f²–4f–4f+16 Apply the distributive property (FOIL)

f²–8f+16

Yes, f²–8f+16=(f–4)².

Notice that q²–4q+4 is a perfect square trinomial because it can be written in the form a²–2ab+b², where a is q and b is 2.

a²–2ab+b²

q²–2q . 2+2²

q²–4q+4

Now use the formula for factorising perfect square trinomials.

a²–2ab+b²=(a–b)²

q²–2q . 2+2²=(q–2)²

q²–4q+4=(q–2)²

The factorised form of q²–4q+4 is (q–2)².

Finally, check your work.

(q–2)²

(q–2)(q–2)Expand

q²–2q–2q+4Apply the distributive property (FOIL)

q²–4q+4

Yes, q²–4q+4=(q–2)².