Question

O quadrado da soma dos dois ternos;

1)

(a+b)²


2)

2 . (x - 3) + 4 . (2x + 1)=


3)

(2x + y)²


4)

(2x - 3)²

Answer 1

Explicação passo-a-passo:

.

$(a + b) {}^{2}$

$a {}^{2} + 2ab + b {}^{2}$

.

$2(x - 3) + 4(2x + 1)$

$2x - 6 + 8x + 4$

$10x - 2$

.

$(2x + y) {}^{2}$

$(2x) {}^{2} + 2 \times 2xy + y {}^{2}$

$4x {}^{2} + 4xy + y {}^{2}$

.

$(2x - 3) {}^{2}$

$(2x) {}^{2} - 2 \times 2x \times 3 + 3 {}^{2}$

$4x {}^{2} - 12x + 9$

Answer 2

Resposta:

$\left(a+b\right)^2\\\\\mathrm{Aplique\:a\:formula\:do\:quadrado\:perfeito}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\\\a=a,\:\:b=b\\\\a^2+2ab+b^2$

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$2\left(x-3\right)+4\left(2x+1\right)\\\\2\left(x-3\right)=2x-6\\\\=2x-6+4\left(2x+1\right)\\\\4\left(2x+1\right)=8x+4\\\\=2x-6+8x+4\\\\2x-6+8x+4=10x-2\\\\=10x-2$

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$\left(2x+y\right)^2\\\\\mathrm{Aplique\:a\:formula\:do\:quadrado\:perfeito}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\\\a=2x,\:\:b=y\\\\=\left(2x\right)^2+2\cdot \:2xy+y^2\\\\\left(2x\right)^2+2\cdot \:2xy+y^2=4x^2+4xy+y^2\\\\=4x^2+4xy+y^2$

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$\left(2x-3\right)^2\\\\\mathrm{Aplique\:a\:formula\:do\:quadrado\:perfeito}:\quad \left(a-b\right)^2=a^2-2ab+b^2\\\\a=2x,\:\:b=3\\\\=\left(2x\right)^2-2\cdot \:2x\cdot \:3+3^2\\\\\left(2x\right)^2-2\cdot \:2x\cdot \:3+3^2=4x^2-12x+9\\\\=4x^2-12x+9$