Expand \(5(x+2)\).

Factor \(6x+18\) by taking out the greatest common factor.

Expand \((x+4)(x+3)\).

Factor \(x^2-49\).

Expand and simplify \(3(2x-5)-2(x+4)\).

Factor \(x^2+9x+20\).

Expand \((2x-3)^2\).

Factor \(2x^2+7x+3\).

Complete the square for \(x^2+8x+5\).

Simplify \(\frac{x^2-16}{x-4}\), stating any restriction on \(x\).

Show by expansion that \((x+2)(x-5)=x^2-3x-10\).

A student expands \((x-6)^2\) as \(x^2-36\). Explain the mistake and give the correct expansion.

Rewrite \(2x^2-12x+7\) in completed-square form.

Factor completely: \(3x^3-12x\).

Find values of \(k\) for which \(x^2+kx+16\) is a perfect-square trinomial.

Simplify \(\frac{x^2+5x+6}{x^2+x-6}\), stating all excluded values of \(x\).

Choose the most useful form of \(x^2-10x+21\) for finding its minimum value, then find that minimum.

Prove the identity \((a+b)^2-(a-b)^2=4ab\).

A simplification gives \(\frac{x^2-1}{x-1}=x+1\). Explain why this is not equivalent to the original expression for every real \(x\).

Factor \(x^4-13x^2+36\) completely over the real numbers.