Sawa, Mbari. Haya hapa maswali mawili ya mwisho ya kuweka katika vigawo. a) Weka 9x² − 12x + 4 katika vigawo. Step 1: Tambua kuwa huu ni mraba kamili wa trinomial. Usemi huu una fomu a²x² − 2abx + b². Hapa, a²x² = 9x² ⇒ ax = 3x. Na b² = 4 ⇒ b = 2. Step 2: Thibitisha neno la kati. Neno la kati linapaswa kuwa −2abx = −2(3x)(2) = −12x. Hii inalingana na usemi wetu. Step 3: Andika usemi katika vigawo. 9x² − 12x + 4 = (3x − 2)² Jibu: (3x−2)² b) Weka x³ − 8 katika vigawo. Step 1: Tambua kuwa huu ni tofauti ya ujazo (difference of cubes). Fomula ya tofauti ya ujazo ni a³ − b³ = (a−b)(a² + ab + b²). Hapa, a³ = x³ ⇒ a = x. Na b³ = 8 ⇒ b = 2. Step 2: Tumia fomula ya tofauti ya ujazo. x³ − 8 = (x − 2)(x² + x · 2 + 2²); x³ − 8 = (x − 2)(x² + 2x + 4) Jibu: (x−2)(x²+2x+4)

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9x2 - 12x + 4 x3 - 8

June 30, 2026Mathematics

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2 parts

(3x-2)^2

(x-2)(x^2+2x+4)

Step-by-step solution

5 steps

Sawa, Mbari. Haya hapa maswali mawili ya mwisho ya kuweka katika vigawo.

Part a· 3 steps

Weka $9x^2 - 12x + 4$ katika vigawo.

Tambua kuwa huu ni mraba kamili wa trinomial.
Usemi huu una fomu $a^2x^2 - 2abx + b^2$ .
Hapa, $a^2x^2 = 9x^2 \implies ax = 3x$ .
Na $b^2 = 4 \implies b = 2$ .
Thibitisha neno la kati.
Neno la kati linapaswa kuwa $-2abx = -2(3x)(2) = -12x$ . Hii inalingana na usemi wetu.
Andika usemi katika vigawo.
$9x^2 - 12x + 4 = (3x - 2)^2$
Jibu: $\boxed{(3x-2)^2}$

Part b· 2 steps
$(x-2)(x^2+2x+4)$

Weka $x^3 - 8$ katika vigawo.

Tambua kuwa huu ni tofauti ya ujazo (difference of cubes).
Fomula ya tofauti ya ujazo ni $a^3 - b^3 = (a-b)(a^2 + ab + b^2)$ .
Hapa, $a^3 = x^3 \implies a = x$ .
Na $b^3 = 8 \implies b = 2$ .
Tumia fomula ya tofauti ya ujazo.
$x^3 - 8 = (x - 2)(x^2 + x \cdot 2 + 2^2)$ $x^3 - 8 = (x - 2)(x^2 + 2x + 4)$
Jibu: $\boxed{(x-2)(x^2+2x+4)}$

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9x2 - 12x + 4 x3 - 8

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Step-by-step solution

Part a· 3 steps

Tambua kuwa huu ni mraba kamili wa trinomial.

Thibitisha neno la kati.

Andika usemi katika vigawo.

Part b· 2 steps(x−2)(x2+2x+4)(x-2)(x^2+2x+4)(x−2)(x2+2x+4)

Tambua kuwa huu ni tofauti ya ujazo (difference of cubes).

Tumia fomula ya tofauti ya ujazo.

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Part b· 2 steps
$(x-2)(x^2+2x+4)$