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a) (a+b)(a+b)
=\(a^2+ab+ab+b^2\)
=\(a^2+\left(ab+ab\right)+b^2\)
=\(a^2+2ab+b^2\)
=\(aa+2ab+bb\)
b) (a-b)(a-b)
=\(a^2-ab-ab+b^2\)
=\(a^2+\left(-ab-ab\right)+b^2\)
=\(a^2-2ab+b^2\)
c) (a+b)(a-b)
=\(a^2-ab+ab-b^2\)
=\(a^2+\left(-ab+ab\right)-b^2\)
=\(a^2-b^2\)
a. \(A=5a^3b^4\)
\(=5.\left(-2\right)^3.1^4\)
\(=5.\left(-8\right).1\)
\(=-40\)
b.\(B=9a^5b^2\)
\(=9.\left(-1\right)^5.\left(-2\right)^2\)
\(=9.\left(-1\right).4\)
\(=-36\)
Giải thích
(a + b)(a - b)
= (a + b)a - (a + b)b
= (a.a + b.a) - (a.b + b.b)
= a.a + b.a - a.b - b.b
= a2 + b.a - a.b - b2
= a2 + (b.a - a.b) - b2
= a2 + 0 - b2
= a2 - b2
2 . Tìm GTLN :
b . \(B=-\left|2019-x\right|+2018\)
\(\Rightarrow B=2018-\left|2019-x\right|\)
Vì \(\left|2019-x\right|\ge0\forall x\)
\(\Rightarrow B=2018-\left|2019-x\right|\le2018\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow\left|2019-x\right|=0\)
\(\Leftrightarrow2019-x=0\)
\(\Leftrightarrow x=2019-0\)
\(\Leftrightarrow x=2019\)
Vậy \(B_{max}=2018\Leftrightarrow x=2019\)
a)\(\left(a+b\right)\left(a-b\right)-a^2+b^2\)
\(=a^2-b^2-a^2+b^2=0\)
b)\(\left(-a+b\right)\left(a-b\right)+a^2+b^2\)
\(=-a^2+2ab-b^2+a^2+b^2=2ab\)
c)\(a\left(b+c\right)-b\left(c-a\right)+c\left(b-a\right)\)
\(=ab+ac+ab-bc+bc-ac\)
\(=ab+ab=2ab\)
d)\(\left(a+b\right)\left(c+d\right)-\left(a-b\right)\left(c-d\right)\)
\(=ac+ad+bc+bd-ac+ad+bc-bd\)
\(=2ad+2bc=2\left(ad+bc\right)\)
Đặt a/b = x ; b/a = y cho dẽ
a) A = ( x - y )( x^2 + y^2 - xy )
= x^3 + xy^2 - x^2y - x^2y - y^3 + xy^2
= x^3 - y^3
= (a/b)^3 - (b/a)^3
b)\(B=\left(\frac{a}{b}+\frac{b}{a}\right).\left(\frac{a}{b}-\frac{b}{a}\right)\)
\(=>B=\frac{a}{b}^2-\frac{b}{a}^2\)
\(=>B=\frac{a^2}{b^2}-\frac{b^2}{a^2}\)
\(=>B=\frac{a^4-b^4}{a^2.b^2}\)