Latihan Bentuk Aljabar 01

\(2x^2 + 5xy + 1 = 2(-1)^2 + 5(-1)(2) + 1\)

\(2x^2 + 5xy + 1 = 2(1) + 5(-2) + 1\)

\(2x^2 + 5xy + 1 = 2 \:-\:10  + 1\)

\(2x^2 + 5xy + 1 = -7\)

Note:

\(\color{red} (-1)^2 = -1 \times -1 = + 1\)

\(\dfrac{5p^3 + 4r^2}{5q + 1} = \dfrac{5(-2)^3 + 4(-3)^2}{5(1) \:-\: 1} \)

\(\dfrac{5p^3 + 4r^2}{5q + 1} = \dfrac{5(-8) + 4(9)}{4} \)

\(\dfrac{5p^3 + 4r^2}{5q + 1} = \dfrac{-40 + 36}{4} \)

\(\dfrac{5p^3 + 4r^2}{5q + 1} = \dfrac{-4}{4} \)

\(\dfrac{5p^3 + 4r^2}{5q + 1} = -1\)

Note:

\(\color{red} (-2)^3 = -2 \times -2 \times -2 = -8\)

\(\color{red} (-3)^2 = -3 \times -3  = 9\)

\(7x + 3y \:-\:3(x \:-\:6y)\:-\:x + 2z\)

Buka kurung

\(7x + 3y \:-\:3x + 18y\:-\:x + 2z\)

Kumpulkan suku-suku yang sejenis

\(7x\:-\:3x \:-\:x + 3y + 18y + 2z\)

\((7\:-\:3\:-\:1)x + (3 + 18)y + 2z\)

\(3x +21y + 2z\)

\(\dfrac{1}{2}(4x + 6y)\:-\:\dfrac{2}{5}(10x \:-\:5y)\)

Buka kurung

\(\dfrac{1}{2} \cdot 4x + \dfrac{1}{2} \cdot 6y \:-\:\dfrac{2}{5} \cdot 10x + \dfrac{2}{5}\cdot 5y\)

\(2x + 3y\:-\:4x + 2y\)

\(2x\:-\:4x + 3y + 2y\)

\((2\:-\:4)x + (3 + 2)y\)

\(-2x + 5y\)

\(2a^2 + 3ab + 3a \:-\: b^2 + 6ab + 3b\)

Kumpulkan suku-suku yang sejenis

\(2a^2 \:-\:b^2 + 3ab + 6ab + 3a + 3b\)

\(2a^2 \:-\:b^2 + 9ab + 3a + 3b\)

\(\dfrac{5x^2}{5y^2} \times \dfrac{3x^3}{y^5} = \dfrac{5x^2\cdot 3x^3}{5y^2 \cdot y^5}\)

\(\dfrac{5x^2}{5y^2} \times \dfrac{3x^3}{y^5} = \dfrac{15x^2\cdot x^3}{5y^2 \cdot y^5}\)

Gunakan sifat eksponen \(\color{red}x^m \cdot x^n = x^{m + n}\)

\(\dfrac{5x^2}{5y^2} \times \dfrac{3x^3}{y^5} = \dfrac{15x^{2 + 3}}{5y^{2 + 5}}\)

\(\dfrac{5x^2}{5y^2} \times \dfrac{3x^3}{y^5} = \dfrac{\cancelto{3}{15}x^{5}}{\cancel{5}y^{7}}\)

\(\dfrac{5x^2}{5y^2} \times \dfrac{3x^3}{y^5} = \dfrac{3x^{5}}{y^{7}}\)

\(\dfrac{7ab^2}{2b} \div \dfrac{49b}{6b^2}\) dapat ditulis \(\dfrac{7ab^2}{2b}\times \dfrac{6b^2}{49b}\)

\(\dfrac{7ab^2}{2b}\times \dfrac{6b^2}{49b} = \dfrac{\cancel{7}ab^2 \cdot \cancelto{3}{6}b^2 }{\cancel{2}b \cdot \cancelto{7}{49}b}\)

\(\dfrac{7ab^2}{2b}\times \dfrac{6b^2}{49b} = \dfrac{3ab^2 \cdot b^2 }{7b \cdot b}\)

Gunakan sifat eksponen \(\color{red}x^m \cdot x^n = x^{m + n}\)

\(\dfrac{7ab^2}{2b}\times \dfrac{6b^2}{49b} = \dfrac{3ab^{2 + 2} }{7b^{1 + 1}}\)

\(\dfrac{7ab^2}{2b}\times \dfrac{6b^2}{49b} = \dfrac{3ab^4 }{7b^2}\)

Gunakan sifat eksponen \(\color{red} \dfrac{x^m}{x^n} = x^{m\:-\:n}\)

\(\dfrac{7ab^2}{2b}\times \dfrac{6b^2}{49b} = \dfrac{3ab^{4\:-\:2} }{7}\)

\(\dfrac{7ab^2}{2b}\times \dfrac{6b^2}{49b} = \dfrac{3ab^2 }{7}\)

\(\dfrac{7ab^2}{2b}\times \dfrac{6b^2}{49b} = \dfrac{3}{7}ab^2\)