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ÖRNEKLER: 10 TANE CEBİRSEL İFADELERİ ÇARPMA ÖRNEĞİ

Aşağıda cebirsel ifadelerin çarpımı ile ilgili örnekler bulabilirsiniz.

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ÖRNEK 1:

(x – 1)(y – 1) = x . y + x . (–1) + (–1) . y + (–1) . (–1)

= xy – x – y + 1

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ÖRNEK 2:

(1 – x)(1 – y) = 1 . 1 + 1 . (–y) + (–x) . 1 + (–x) . (–y)

= 1 – y – x + xy

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ÖRNEK 3:

(2x + y)(2x + y) = 2x . 2x + 2x . y + y . 2x + y . y

= 4x² + 2xy + 2xy + y²

= 4x² + 4xy + y²

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ÖRNEK 4:

(x + 1)(x + 1) = x . x + x . 1 + 1 . x + 1 . 1

= x² + 2x + 1

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ÖRNEK 5:

(x + 3)(xy + 1) = x . xy + x . 1 + 3 . xy + 3 . 1

= x²y + x + 3xy + 3

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ÖRNEK 6:

(12x – 3y)(–5xy) = 12x . (–5xy) + (–3y) . (–5xy)

= –60x²y + 15xy²

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ÖRNEK 7:

–c(–a – b) = (–c) . (–a) + (–c) . (–b)

= ca + cb

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ÖRNEK 8:

x(1 – x) = x . 1 + x . (–x)

= x – x²

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ÖRNEK 9:

(a² – 1)(a² + 1) = a² . a² + a² . 1 + (–1) . a² + (–1) . 1

= a⁴ + a² – a² – 1

= a⁴ – 1

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ÖRNEK 10:

(2a – b)(a – 2b) = 2a . a + 2a . (–2b) + (–b) . a + (–b) . (–2b)

= 2a² – 4ab – ab + 2b²

= 2a² – 5ab + 2b²

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