multiply (a+b) (a+b) (a+b)
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Answer:
We will find this product using the formula: (a-b)(a+b)=a2- b2 Here a=300 and b=3. Then we get: (300-3) × (300+3) =3002 - 32 = 90000-9 = 89991. Therefore, 297 × 303 = 89991. Example 3: Find the roots of the quadratic equation x2+5x+6=0 using algebra formulas for quadratic equations.
a×(b+c)=(a×b)+(a×c)" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">a×(b+c)=(a×b)+(a×c)a×(b+c)=(a×b)+(a×c)
(b+c)×a=(b×a)+(c×a)" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">(b+c)×a=(b×a)+(c×a)(b+c)×a=(b×a)+(c×a)
So in this case:
(a+b)×(a+b)=[(a+b)×a]+[(a+b)×b]=[a×a+b×a]+[a×b+b×b]=a2+2ab+b2" role="presentation" style="display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">(a+b)×(a+b)=[(a+b)×a]+[(a+b)×b]=[a×a+b×a]+[a×b+b×b]=a2+2ab+b2(a+b)×(a+b)=[(a+b)×a]+[(a+b)×b]=[a×a+b×a]+[a×b+b×b]=a2+2ab+b2
So basically, you multiply all combinations and you add everything:
More generic:
(a+b)×(c+d)=ac+ad+bc+bd" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">(a+b)×(c+d)=ac+ad+bc+bd(a+b)×(c+d)=ac+ad+bc+bd
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Maham Aizaz
, B.S. Mathematics, Lahore University of Management Sciences (2022)
Answered June 26, 2018
You can multiply each term separately like this:
(a+b)(a+b) = a x a +a x b + b x a + bx b = a^2 + ab + ba + b^2 = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2
0R
You can multiply the second bracket with each term of the first one:
(a+b)(a+b) = a(a+b) + b(a+b) = a^2 + ab + ba + b^2 = a^2 + 2ab + b^2
0R
You can add the exponents and apply the square formula:
(a+b)(a+b) = (a+b)^2 = (a)^2 + 2 (a)(b) + (b)^2 = a^2 + 2ab + b^2
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