**1. Multiplying a Binomial by a Binomial**

We use the distributive law of multiplication in this case. Multiply each term of a binomial with every term of another binomial. After multiplying the polynomials we have to look for the like terms and combine them.

**Example**

Simplify (3a + 4b) × (2a + 3b)

**Solution:**

(3a + 4b) × (2a + 3b)

= 3a × (2a + 3b) + 4b × (2a + 3b) [distributive law]

= (3a × 2a) + (3a × 3b) + (4b × 2a) + (4b × 3b)

= 6 a^{2 }+ 9ab + 8ba + 12b^{2}

= 6 a^{2} + 17ab + 12b^{2} [Since ba = ab]

**2. Multiplying a Binomial by a Trinomial**

In this also we have to multiply each term of the binomial with every term of trinomial.

**Example**

Simplify (p + q) (2p – 3q + r) – (2p – 3q) r.

**Solution:**

We have a binomial (p + q) and one trinomial (2p – 3q + r)

(p + q) (2p – 3q + r)

= p(2p – 3q + r) + q (2p – 3q + r)

= 2p^{2} – 3pq + pr + 2pq – 3q^{2} + qr

= 2p^{2} – pq – 3q^{2} + qr + pr

Therefore,

(p + q) (2p – 3q + r) – (2p – 3q) r

= 2p^{2} – pq – 3q^{2} + qr + pr – (2pr – 3qr)

= 2p^{2} – pq – 3q^{2} + qr + pr – 2pr + 3qr

= 2p^{2} – pq – 3q^{2} + (qr + 3qr) + (pr – 2pr)

= 2p^{2} – 3q^{2} – pq + 4qr – pr

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