Chapter 3

Use the difference-of-squares pattern to factor each of the following. $$4 x^{2}-(y+1)^{2}$$

Factor each of the composite numbers into the product of prime numbers. For example, \(30=2 \cdot 3 \cdot 5 .\) $$56$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(y-5)(y+11)$$

Find each product. $$\left(\frac{2}{5} x y^{2}\right)\left(\frac{3}{4} x^{2} y^{4}\right)$$

Add the given polynomials. \(3 x^{2}-5 x-1\) and \(-4 x^{2}+7 x-1\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$25 x^{2}+30 x+8=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$x^{2}-14 x y+40 y^{2}$$

Use the difference-of-squares pattern to factor each of the following. $$x^{2}-(y-5)^{2}$$

Factor each of the composite numbers into the product of prime numbers. For example, \(30=2 \cdot 3 \cdot 5 .\) $$64$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(y-3)(y+9)$$

Find each product. $$\left(\frac{1}{2} x^{2} y^{6}\right)\left(\frac{2}{3} x y\right)$$

Add the given polynomials. \(6 x^{2}+8 x+4\) and \(-7 x^{2}-7 x-10\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$3 t(t-4)=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$a^{2}-a b-56 b^{2}$$

Use the difference-of-squares pattern to factor each of the following. $$9 a^{2}-(2 b+3)^{2}$$

Factor each of the composite numbers into the product of prime numbers. For example, \(30=2 \cdot 3 \cdot 5 .\) $$72$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(n+2)(n-7)$$

Find each product. $$\left(-\frac{3}{4} a b\right)\left(\frac{1}{5} a^{2} b^{3}\right)$$

Add the given polynomials. \(12 a^{2} b^{2}-9 a b\) and \(5 a^{2} b^{2}+4 a b\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$1-x^{2}=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$a^{2}+2 a b-63 b^{2}$$

Use the difference-of-squares pattern to factor each of the following. $$16 s^{2}-(3 t+1)^{2}$$

Factor each of the composite numbers into the product of prime numbers. For example, \(30=2 \cdot 3 \cdot 5 .\) $$84$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(n+3)(n-12)$$

Find each product. $$\left(-\frac{2}{7} a^{2}\right)\left(\frac{3}{5} a b^{3}\right)$$

Add the given polynomials. \(15 a^{2} b^{2}-a b\) and \(-20 a^{2} b^{2}-6 a b\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$-6 n^{2}+13 n-2=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$15 x^{2}+23 x+6$$

Use the difference-of-squares pattern to factor each of the following. $$(x+2)^{2}-(x+7)^{2}$$

Factor each of the composite numbers into the product of prime numbers. For example, \(30=2 \cdot 3 \cdot 5 .\) $$87$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(x+6)(x-6)$$

Find each product. $$\left(-\frac{1}{2} x y\right)\left(\frac{1}{3} x^{2} y^{3}\right)$$

Add the given polynomials. \(2 x-4,-7 x+2\), and \(-4 x+9\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$(x+1)^{2}-4=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$9 x^{2}+30 x+16$$

Use the difference-of-squares pattern to factor each of the following. $$(x-1)^{2}-(x-8)^{2}$$

Factor each of the composite numbers into the product of prime numbers. For example, \(30=2 \cdot 3 \cdot 5 .\) $$91$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(t+8)(t-8)$$

Find each product. $$\left(\frac{3}{4} x^{4} y^{5}\right)\left(-x^{2} y\right)$$

Add the given polynomials. \(-x^{2}-x-4,2 x^{2}-7 x+9\), and \(-3 x^{2}+6 x-10\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$2 n^{3}=72 n$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$12 x^{2}-x-6$$

Factor each of the following polynomials completely. Indicate any that are not factorable using integers. Don't forget to look first for a common monomial factor. $$9 x^{2}-36$$

Factor completely. $$6 x+3 y$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(x-6)^{2}$$

Find each product. $$(3 x)\left(-2 x^{2}\right)\left(-5 x^{3}\right)$$

Subtract the polynomials using the horizontal format. \(5 x-2\) from \(3 x+4\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$a(a-1)=2$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$20 x^{2}-11 x-3$$

Factor each of the following polynomials completely. Indicate any that are not factorable using integers. Don't forget to look first for a common monomial factor. $$8 x^{2}-72$$