Exponents and Polynomials

Multiplying Binomials (FOIL)

Multiply two binomials using FOIL: First, Outer, Inner, Last. Each term in the first binomial multiplies every term in the second. Combine the middle terms (Outer + Inner) to get the final trinomial.

multiply-binomials-foil FOIL is systematic: F gives the x^2 term, O and I give the x terms that combine, L gives the constant. Always combine O+I.

Example

Build the four FOIL products, then combine the middle terms.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

(2x+3)(x+2)( 2x + 3 )( x+ 2 )

Step 2 — First

First product: 2 x 1 = 2.

2x×x=2x22x \times x= \hlmath{2x^{2}}

Step 3 — Outer

Outer product: 2 x 2 = 4.

2x×2=4x2x \times 2 = \hlmath{4x}

Step 4 — Inner

Inner product: 3 x 1 = 3.

3×x=3x3 \times x= \hlmath{3x}

Step 5 — Last

Last product: 3 x 2 = 6.

3×2=63 \times 2 = \hl{6}

Step 6 — Combine middle terms

Combine middle terms: 4 + 3 = 7.

4+3=74 + 3 = \hl{7}

Step 7 — Result

Read the final result.

2x2+7x+62x^{2} + 7x + 6