...the square of a + b (Art. 11), and the result may be expressed in words, as follows : " The square of the sum of two quantities is equal to the sum of the squares of the two quantities, together with twice their product.1"* (2) To find the square of a +...

...+ 4a62) = 49a«6s — 16а»ЬЧ The following properties are also of great use : — 1. The square of the sum of two quantities, is equal to the sum of their squares plus twice their product. Let a and b be the quantities, then a -fb is theipsum, and...

...a+»(31.) 2. Find the square of a — x (179.) It appears from these two examples that — 1The square of the sum of two quantities is equal to the sum of the squares of these quantities and twice their product; and, The square of the difference of two quantities...

...20, and b — 8 ; then a + b = 28. a + b ab a2 + ab + ab + Hence it appears, that the second power of the sum of two quantities is equal to the sum of their second powers, increased by twice their product. 19. What is the second power of a — b 1 a...

...to the difference of the squares of those quantities." From the 2nd of these we see that "The square of the sum of two quantities, is equal to the sum of their squares, plus twice their product." From the 3rd of these we see that "The square of the difference...

...3a，6+3a6，+&' =a>+b，+8ab(a+b) =a'-が-3aあ(a-あ). Hence， by the last two formul，e， the cube of the sum of two quantities is equal to the sum of their cubes + three times their product multiplied by their sum. ⅠⅠ ノ 石 Ⅹ ノ 圧 言 二...

...formula [sec. 1, 1], — For, the result of the multiplication may be read as follows : — " the square of the sum of two quantities is equal to the sum of their squares, plus twice their product." And as the given quantities may represent any possible ones,...

...(a— a) 1 What is the Product of (a+5) (a— 5) 1 Of (3+y) (3— y)1 Of (x— 1) (a (59.) The Square of the sum of two quantities is equal to the sum of the squares plus twice the product of the two quantities. Thus (a+b) (a+b), that is, the square of a+b,...

...Multiply (а + и)2 by (а - о)3. Ans. а5 — а4о — 2asô2 + 2asô3 + ai4 — б5. 71. The square of the sum of two quantities is equal to the sum of their squares increased by twice their product. If we multiply a + Ъ by a + b %e obtain a2 + 2ab +...

...у. ix. (x — у)» = x3 — yс1y + усy2 — y3. i. (a + b) (a + ¿) = a" + P + 2ab. The Square of the sum of two quantities is equal to the sum of the squares of each of the quantities increased by twice the product. Write down the squrtres of 1. a +...