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nydus/The First Steps in AlgebraPublic

This textbook introduces the fundamental concepts of algebra, including definitions of units, quantities, and number symbols. It explains the use of letters to represent numbers and outlines the signs for basic mathematical operations.

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Table of Contents

Special Rules.

$(a - 3 b)^{2}$ .

$(2 x - y)^{2}$ .

$(y - 2 x)^{2}$ .

$(a + 5 b)^{2}$ .

$(2 a - 5 c)^{2}$ .

$(x + y) (x - y)$ .

$(4 a - b) (4 a + b)$ .

$(2 b - 3 c) (2 b + 3 c)$ .

$(x + 5 b) (x + 5 b)$ .

$(y - 2 z) (y - 2 z)$ .

$(y + 3 z) (y - 3 z)$ .

$(2 a - 3 b) (2 a + 3 b)$ .

$(2 a - 3 b) (2 a - 3 b)$ .

$(2 a + 3 b) (2 a + 3 b)$ .

$(5 x + 3 a) (5 x - 3 a)$ .

96. Product of Two Binomials of the Form $x + a$, $x + b$.

The product of two binomials which have the form $x + a$ , $x + b$ , should be carefully noticed and remembered.

Each of these results has three terms.

The first term of each result is the product of the first terms of the binomials.

The last term of each result is the product of the second terms of the binomials.

The middle term of each result has for a coefficient the algebraic sum of the second terms of the binomials.

The intermediate step given above may be omitted, and the products written at once by inspection. Thus,

Multiply $x + 8$ by $x + 7$ .

$& 8 + 7 = 15, 8 \times 7 = 56 . ∴ & (x + 8) (x + 7) = x^{2} + 15 x + 56 .$

Multiply $x - 8$ by $x - 7$ .

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