Pembahasan Soal Buku Paket/BSE Matematika SMP Kelas 8 Halaman 15 (Kurikulum Merdeka)
Berikut ini mimin sajikan pembahasan beberapa soal Buku Paket/BSE matematika SMP kelas 8 halaman 15 (kurikulum merdeka). Selamat membaca, sobat. Semoga bermanfaat.
Soal nomor 1
Jawab:
$\begin{aligned} (1).&2x+3y+7x+5y\\&=2x+7x+3y+5y \\&= (2+7)x+(3+5)y\\&=9x+8y\\ \\(2).&-4a+8b-2a-5b\\&= -4a-2a+8b-5b\\&= (-4-2)a+(8-5)b\\&=-6a+3b\\ \\(3).& 5a^2+a^2\\&= (5+1)a^2\\&=6a^2\\ \\ (4).&3x^2-6x+1-2x^2+4x\\&= 3x^2-2x^2-6x+4x +1\\&= (3-2)x^2+(-6+4)x+1\\&= x^2-2x+1\\ \\ (5).& (7a+b)+(-9a+8b)\\&= 7a+b-9a+8b\\&= 7a-9a+b+8b\\&= (7-9)a+(1+8)b\\&= -2a+9b\\ \\(6).&(-3x^2-4x)+(5x^2-x)\\&= -3x^2-4x+5x^2-x\\&=-3x^2+5x^2-4x-x\\&= (-3+5)x^2+(-4-1)x\\&= 2x^2-5x\\ \\ (7).&(8x-6y)-(2x+4y)\\&= 8x-6y-2x-4y\\&=8x-2x-6y-4y\\&= (8-2)x+(-6-4)y\\&=6x-10y\\ \\ (8).&(-x^2+9x+6)-(7x^2-5x+8)\\&= -x^2+9x+6-7x^2+5x-8\\&= -x^2-7x^2+9x+5x+6-8\\&= (-1-7)x^2+(9+5)x-2\\&= -8x^2+14x-2\\ \\ (9). &2x-6y-5+3x+2y-4\\&= 2x+3x-6y+2y-5-4\\&= (2+3)x+(-6+2)y-9\\&= 5x-4y-9\\ \\ (10).& (-5x+8y)-(4x-7y)\\&= -5x+8y-4x+7y\\&=-5x-4x+8y+7y\\&= (-5-4)x+(8+7)y\\&=-9x+15y \end{aligned}$
Soal nomor 2
Jawab:
$\begin{aligned} (1).&2(6a-5b+1)\\&= 12a-10b+2\\ \\ (2).&(9x-4y) \times (-3)\\&= -27x+12y\\ \\ (3).&(20a+16b):4\\&= (20a+16b) \times \frac{1}{4}\\&= 5a+4b\\ \\ (4).& \frac{8x+12y}{-2}\\&= \frac{8x}{-2}+\frac{12y}{-2}\\&= -4x-6y \end{aligned}$
Soal nomor 3
Jawab:
$\begin{aligned} (1).&3(a+2b)+6(a-b)\\&= 3a+6a+6b-6b\\&=(3+6)a+(6-6)b\\&= 9a\\ \\ (2).&-(5x-y)+4(3x-y)\\&= -5x+y+12x-4y\\&= -5x+12x+y-4y \\&= (-5+12)x+(1-4)y\\&= 7x-3y\\ \\ (3).& 2(4x+y)-7x\\&= 8x+2y-7x\\&= 8x-7x+2y\\&= (8-7)x+2y\\&= x+2y\\ \\ (4).& 8a-5b-3(a-4b)\\&= 8a-5b-3a+12b\\&=8a-3a-5b+12b\\&= (8-3)a+(-5+12)b\\&= 5a+7b\\ \\ (5).&4(2x-y)-2(x-y+1)\\&= 8x-4y-2x+2y-2\\&= 8x-2x-4y+2y-2\\ &= (8-2)x+(-4+2)y-2\\&= 6x-2y-2 \\ \\ (6).& \frac{1}{4}(a-3b)-\frac{1}{6}(2a-3b)\\&=\frac{1}{4}a-\frac{3}{4}b-\frac{2}{6}a+\frac{3}{6}b\\&=\frac{-a-3b}{12}\\ \\ (7). &\frac{2a-b}{6}+\frac{a+b}{8}\\&= \frac{8(2a-b)+6(a+b)}{48}\\&= \frac{16a-8b+6a+6b}{48}\\&= \frac{22a-2b}{48}\\&= \frac{11a-b}{24}\\ \\ (8).& \frac{4x-y}{3}-\frac{x-3y}{2}\\&= \frac{2(4x-y)-3(x-3y)}{6}\\&=\frac{8x-2y-3x+9y}{6}\\&= \frac{5x+7y}{6}\\ \\ (9).&x-\frac{x+5y}{2}\\&= \frac{2x}{2}-\frac{x+5y}{2}\\ &= \frac{2x-x-5y}{2}\\&= \frac{x-5y}{2} \end{aligned}$
Soal nomor 4
Jawab:
$\begin{aligned} (1).&9a \times (-5b)\\&= 9 \times a \times (-5) \times b \\&=-45ab\\ \\ (2).& 12x \times \frac{5}{6}y\\ &= 12 \times x \times \frac{5}{6} \times y \\&= 10xy\\ \\ (3).&3x^2 \times 7x\\&= 3 \times x \times x \times 7 \times x \\&= 21 x^3\\ \\ (4).&(-7a)^2\\&= (-7a) \times (-7a)\\&= -7 \times a \times -7 \times a\\&= 49a^2\\ \\ (5).&4a \times (-ab)\\&= 4 \times a \times -a \times b\\&= -4a^2b\\ \\ (6).&(-18xy):(-9x)\\&= (-18xy) \times -\frac{1}{9x}\\ &= -18 \times x \times y \times -\frac{1}{9x}\\&= 2y\\ \\ (7).&x^3:x\\&= x^3 \times \frac{1}{x}\\&= x \times x \times x \times \frac{1}{x}\\&= x^2 \\ \\ (8).&6x^2:\frac{3}{4}x\\&= 6x^2 \times \frac{4}{3x}\\&= 6 \times x \times x \times \frac{4}{3x}\\&= 8x\\ \\ (9).&x^2 \times 4x : 8xy\\&= x^2 \times 4x \times \frac{1}{8xy}\\&= \frac{x^2}{2y}\\ \\ (10). &15a^2b:(-6ab^2) \times 2ab\\&= 15a^2b \times -\frac{1}{6ab^2} \times 2ab\\&= -5a^2 \end{aligned}$
Soal nomor 5
Jawab:
$\begin{aligned} (1).&a^2-b\\&= (-3)^2-8\\&=9-8\\&=1\\ \\ (2).&8x^2y^3:4xy^2\\&= 8x^2y^3 \times \frac{1}{ 4xy^2}\\&= 2xy\\&= 2 \times 2 \times (-5) \\&= -20\\ \\ (3).& (3a+b)-(a+4b)\\&= 3a+b-a-4b\\&= 2a-3b\\&= 2 \times \frac{1}{2}-3 \times (-1)\\&=1+3\\&=4 \end{aligned}$
Demikianlah pembahasan beberapa soal Buku Paket/BSE matematika SMP kelas 8 halaman 15 (kurikulum merdeka). Semoga bermanfaat.
Referensi
Tim Gakko Tosho. 2021. Matematika untuk Sekolah Menengah Pertama Kelas VIII . Jakarta: Kementerian Pendidikan, Kebudayaan, Riset, dan Teknologi.
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