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nydus/The First Steps in AlgebraPublic

Page 64 of 226

Table of Contents

Special Rules.

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

Multiply $x - 7 y$ by $x + 6 y$ .

$& - 7 + 6 = - 1, (- 7) \times 6 y = - 42 y^{2} . ∴ & (x - 7 y) (x + 6 y) = x^{2} - x y - 42 y^{2} .$

Multiply $x + 6 y$ by $x - 5 y$ .

$& + 6 - 5 = 1, 6 y \times (- 5 y) = - 30 y^{2} . ∴ & (x + 6 y) (x - 5 y) = x^{2} + x y - 30 y^{2} .$

Exercise 27.

Write by inspection the product of:

$(x + 7) (x + 4)$ .

$(x - 3) (x + 7)$ .

$(x - 2) (x - 4)$ .

$(x - 6) (x - 10)$ .

$(x + 7) (x - 4)$ .

$(x + a) (x - 2 a)$ .

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

$(a + 3 c) (a + 3 c)$ .

$(a + 2 x) (a - 4 x)$ .

$(a - 3 b) (a - 4 b)$ .

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

$(x - 17) (x - 3)$ .

$(x + 6 y) (x - 5 y)$ .

$(3 + 2 x) (3 - x)$ .

$(5 + 2 x) (1 - 2 x)$ .

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

$(a^{2} b^{2} - x^{2}) (a^{2} b^{2} - 5 x^{2})$ .

$(a^{3} b - a b^{3}) (a^{3} b + 5 a b^{3})$ .

$(x^{2} y - x y^{2}) (x^{2} y - 3 x y^{2})$ .

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