...THEOREM II. The square of the difference between two quantities is equal to the square of the ßrst, minus twice the product of the first by the second,...second. Let a represent one of the quantities and b the other : then a — b = their difference. Now, we have from known principles, (a — ¿)2 = (a...

...Thus : a — 6 a— b a2 — ab —a6+6' But a—b is the difference of the quantities a and 6; hence THEOREM II. The square of the difference of two quantities,...first by the second, plus the square of the second. EXAMPLES. 1 (5— 4)2=25— 40+16=1. 2. (2a— 6)2=4a2-4a6+62. 3. (3x- 22/)2=9x2-12xy+4y2. 4. (^-y2)s=x4-2xy+/....

...39. To form the square of a difference a — b, we have That is, the square of the difference between two quantities is equal to the square of the first,...first by the second, plus the square of the second. 1. Form the square of 2a — b. We have (2<z — i)2 = 4a2 — 2. Form the square of 4<zc— be. We...

...39. To form the square of a difference a — b, we have That is, the square of the difference between two quantities is equal to the square of the first, minus twice the product of the Jirst by the second, plus the square of the second. 1. Form the square of 2a — b. We have 2. Form...

...a— b a2 — ab —ab+b' a2— 2ab+b' But a — 6 is the difference of the quantities a and b; hence THEOREM II. The square of the difference of two quantities, is equal to {he square of the first, minus twice the product of the first by the second, plus the square of the...

...ION. 1. (2+5)2=4+20+25=49. ALGEBRAIC THEOREMS. 3 . (oa+iy) 2=aV+2 abxy+tfy*. 4. (ax2+3;i:z3)2 ART. 79. THEOREM II. — The square of the difference of...second. Let a represent one of the quantities, and b the other ; then a — i=their difference ; and (a — 6)X(<* — &)>or (a — 6)2=the square of...

...Thus : a — 6 a— 6 a2 — a6 — ab+V But a—b is the difference of tho quantities a and b ; hence THEOREM II. The square of the difference of two quantities,...first, minus twice the product of the first by the tecond, plus the sqitare of the second. EXAMPLES. 1. (5-4)*=25-40+16=l. 2. (2a— 6)2=4a2 3. (3*—...

...two quantities T " The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second." (la— 5Z>)S= what! " (la— 5Z>)3= 49as— 70ab+25b\" Resolve a2 — b~ into factors 1 What is the...

...—d c2— erf -cd+d2 Product c2— 2cd+d2 The following formula is obtained from this example : — "the square of the difference of two quantities is equal to the sum of their squares, minus twice their product." 38. EXAMPLE 4 — Multiply a2+2a6+62 By a +b Product...

...the most common mistakes of beginners is to call the square of a+b equal to a'+b'. THEOREM II. (61.) The square of the difference of two quantities is...of the first, minus twice the product of the first and second, plus the square of the second. Thus, if we multiply a — b By a- b a'- ab - ab+b' lVe...